Course Information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2020

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/SX01: Wed 14:50–16:20 D416, D. Smetanová
MAT_1/SX02: Fri 9:40–11:10 D416, D. Smetanová
MAT_1/SX03: Fri 9:40–11:10 D416, D. Smetanová

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

After the successful completing of the course, the student solves basic tasks of the course (counting with vectors, matrices and determinants, solving systems of linear equations, properties and graphs of elementary functions, calculation of limits and function derivation, investigating of function process, counting of primitive functions, idefinite integral, the direct method, per-partes, substitution method, calculation of definite integrals and content of a plane figure) individually.

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Competition
Group Teaching - Cooperation
Group Teaching - Collaboration
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	67
Preparation for the Final Test	20	26
Semester project	20	20
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Presentation	2	2
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
General note: Exitus.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2019

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/P01: Tue 8:00–9:30 E1, D. Smetanová
MAT_1/Q5: Sat 26. 10. 8:00–9:30 E1, 9:40–11:10 E1, Sun 24. 11. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:55 E1, Sat 14. 12. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:10 E1, J. Vysoká
MAT_1/S01: Fri 11:25–12:55 D416, J. Krieg
MAT_1/S02: Fri 13:05–14:35 D416, J. Krieg
MAT_1/S03: Tue 14:50–16:20 A7, F. Šíma
MAT_1/S04: Tue 16:30–18:00 A7, F. Šíma
MAT_1/S05: Thu 8:00–9:30 B5, D. Smetanová
MAT_1/S06: Thu 9:40–11:10 B5, D. Smetanová
MAT_1/S07: Thu 13:05–14:35 B5, D. Smetanová
MAT_1/S08: Thu 14:50–16:20 B5, D. Smetanová

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	89
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Grading of the course: Activity during seminar: maximum 30% (0-30 points), Final Test: maximum 70% (0-70 points). Successful graduates of the course have to get totally at least 70 points: A 100 – 90, B 89,99 – 84, C 83,99 – 77, D 76,99 – 73, E 72,99 – 70, FX 69,99 – 30, F 29,99 - 0.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2019

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (lecturer)

Guaranteed by

Ing. Jaroslav Staněk, DiS.
Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/CCV1: Sun 24. 3. 8:45–12:55 D416, Sun 12. 5. 8:00–9:30 D416, D. Smetanová
MAT_1/CCV2: Fri 5. 4. 9:40–12:55 A1, Fri 26. 4. 9:40–12:55 A1, D. Smetanová

Prerequisites

OBOR(CAP)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	89
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2018

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Vladislav Biba, Ph.D. (seminar tutor)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/P01: Thu 9:40–11:10 E1, D. Smetanová
MAT_1/Q4: Sat 3. 11. 13:50–14:35 B1, 14:50–16:20 B1, 16:30–18:00 B1, Sat 24. 11. 8:00–9:30 B1, 9:40–11:10 B1, 11:25–12:10 B1, Sat 8. 12. 8:00–9:30 B1, 9:40–11:10 B1, 11:25–12:10 B1, D. Smetanová
MAT_1/S01: Fri 9:40–11:10 D516, D. Smetanová
MAT_1/S02: Fri 11:25–12:55 D516, D. Smetanová
MAT_1/S03: Thu 13:05–14:35 B4, D. Smetanová
MAT_1/S04: Mon 9:40–11:10 B4, P. Chládek
MAT_1/S05: Mon 11:25–12:55 B4, P. Chládek
MAT_1/S06: Wed 9:40–11:10 D516, P. Chládek
MAT_1/S07: Tue 14:50–16:20 B3, F. Šíma
MAT_1/S08: Wed 13:05–14:35 D416, F. Šíma

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	89
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2018

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/CCV1: Fri 6. 4. 8:00–12:10 D516, Fri 20. 4. 8:00–12:10 D516, Fri 4. 5. 8:00–12:10 D516, D. Smetanová
MAT_1/CCV2: Sat 17. 3. 8:00–12:55 D416, Sat 14. 4. 13:05–16:20 D415, D. Smetanová

Prerequisites

OBOR(CAP)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.
The capacity limit for the course is 1998 student(s).
Current registration and enrolment status: enrolled: 0/1998, only registered: 0/1998

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2017

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Vladislav Biba, Ph.D. (seminar tutor)
Ing. Jiří Čejka, Ph.D. (seminar tutor)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
Ing. Květa Papoušková (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
Mgr. Michaela Vargová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/P01: Wed 11:25–12:55 E1, D. Smetanová
MAT_1/Q3: Sat 30. 9. 8:00–9:30 B1, 9:40–11:10 B1, 11:25–12:10 B1, Sat 11. 11. 12:10–12:55 B1, 13:05–14:35 B1, 14:50–16:20 B1, 16:30–17:15 B1, Sat 9. 12. 8:00–9:30 B1, 9:40–11:10 B1, D. Smetanová
MAT_1/S01: Tue 13:05–14:35 B5, K. Papoušková
MAT_1/S02: Mon 9:40–11:10 B5, P. Chládek
MAT_1/S03: Mon 14:50–16:20 B5, P. Chládek
MAT_1/S04: Thu 9:40–11:10 B3, V. Biba
MAT_1/S05: Wed 14:50–16:20 D416, F. Šíma
MAT_1/S06: Thu 14:50–16:20 A7, V. Biba
MAT_1/S07: Thu 13:05–14:35 A7, K. Papoušková
MAT_1/S08: Thu 14:50–16:20 D416, V. Biba
MAT_1/S10: Mon 14:50–16:20 B4, P. Chládek
MAT_1/TP01: Tue 9:40–11:10 A219, J. Vysoká
MAT_1/TS01: Tue 11:25–12:55 A219, J. Vysoká

Prerequisites

MAX_KOMBINOVANYCH(999) && MAX_PREZENCNICH(999)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.
The capacity limit for the course is 1998 student(s).
Current registration and enrolment status: enrolled: 0/1998, only registered: 0/1998

Course objectives supported by learning outcomes

The aim of this course is to provide the students with the basic knowledge of algebra, differential and integral calculus of functions of one variable needed in the study of specialized subjects. Then the aim is also to provide and clarify the main methods and algorithms. After the successful completing of the course, the student solves basic tasks of the course (counting with vectors, matrices and determinants, solving systems of linear equations, properties and graphs of elementary functions, calculation of limits and function derivation, investigating of function process, counting of primitive functions, idefinite integral, the direct method, per-partes, substitution method, calculation of definite integrals and content of a plane figure) individually.

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2017

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Tomáš Náhlík, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/P01: Thu 13:05–14:35 E1, D. Smetanová
MAT_1/S01: Fri 9:40–11:10 B4, T. Náhlík
MAT_1/S02: Fri 8:00–9:30 B4, T. Náhlík
MAT_1/S03: Fri 11:25–12:55 B4, T. Náhlík

Prerequisites

FORMA(P)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.
The capacity limit for the course is 120 student(s).
Current registration and enrolment status: enrolled: 0/120, only registered: 0/120

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2016

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Vladislav Biba, Ph.D. (seminar tutor)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. Michaela Vargová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

Timetable of Seminar Groups

MAT_1/P01: Mon 14:50–16:20 E1, M. Vargová
MAT_1/P02: Wed 16:30–18:00 E1, M. Vargová
MAT_1/Q2a: Sat 1. 10. 13:05–14:35 B1, 14:50–16:20 B1, 16:30–18:00 B1, 18:10–19:40 B1, Sun 13. 11. 13:50–14:35 B1, 14:50–16:20 B1, 16:30–18:00 B1, 18:10–19:40 B1, M. Vargová
MAT_1/Q2b: Sat 19. 11. 8:00–9:30 B2, 9:40–11:10 B2, 11:25–12:55 B2, 13:05–14:35 B2, 14:50–15:35 B2, Sat 10. 12. 8:00–9:30 B2, 9:40–11:10 B2, 11:25–12:55 B2, M. Vargová
MAT_1/S01: Tue 14:50–16:20 B5, M. Vargová
MAT_1/S02: Thu 14:50–16:20 E4, J. Vysoká
MAT_1/S03: Tue 11:25–12:55 E7, J. Krieg
MAT_1/S04: Thu 13:05–14:35 D516, J. Krieg
MAT_1/S06: Thu 9:40–11:10 E6, P. Chládek
MAT_1/S08: Mon 11:25–12:55 A6, P. Chládek
MAT_1/S11: Mon 11:25–12:55 E6, D. Smetanová
MAT_1/S12: Wed 13:05–14:35 E6, V. Biba
MAT_1/S13: Tue 8:00–9:30 B5, V. Biba
MAT_1/TP01: Thu 14:50–16:20 A219, M. Vargová
MAT_1/TS01: Thu 13:05–14:35 A219, M. Vargová

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.
The capacity limit for the course is 604 student(s).
Current registration and enrolment status: enrolled: 0/604, only registered: 0/604

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
CHLÁDEK, Petr. Matematika I : studijní opora pro kombinované studium. 1. vyd. České Budějovice: Vysoká škola technická a ekonomická v Českých Budějovicích, 2012, 44 pp. ISBN 978-80-7468-004-5. info

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika I : pro porozumění i praxi : netradiční výklad tradičních témat vysokoškolské matematiky. 2., dopl. vyd. Brno: VUTIUM, 2009, 339 pp. ISBN 978-80-214-3631-2. Obsah info
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
Summer 2016

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Michaela Vargová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/A3: Sat 5. 3. 13:05–14:35 E1, 14:50–16:20 E1, 16:30–18:00 E1, Sat 2. 4. 14:50–16:20 E1, 16:30–18:00 E1, Sat 14. 5. 12:10–12:55 E1, 13:05–14:35 E1, 14:50–16:20 E1, D. Smetanová
MAT_1/P01: Fri 8:00–9:30 E1, D. Smetanová
MAT_1/S01: Fri 9:40–11:10 E7, D. Smetanová
MAT_1/S02: Thu 8:00–9:30 B2, M. Vargová
MAT_1/S03: Wed 8:00–9:30 A4, J. Vysoká
MAT_1/S04: Wed 11:25–12:55 B1, J. Krieg
MAT_1/S05: Wed 8:00–9:30 A7, M. Vacka
MAT_1/S06: Tue 8:00–9:30 B3, M. Vargová
MAT_1/S07: Tue 8:00–9:30 D415, J. Vysoká
MAT_1/S08: Thu 9:40–11:10 A4, J. Krieg
MAT_1/S09: Tue 9:40–11:10 D515, J. Krieg
MAT_1/S10: Thu 13:05–14:35 B3, F. Šíma
MAT_1/S11: Thu 8:00–9:30 B3, J. Vysoká
MAT_1/S12: Thu 13:05–14:35 B2, J. Krieg
MAT_1/S13: Fri 9:40–11:10 E4, M. Vacka

Prerequisites

MAX_KOMBINOVANYCH(210) && MAX_PREZENCNICH(325)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.
The capacity limit for the course is 535 student(s).
Current registration and enrolment status: enrolled: 0/535, only registered: 0/535

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2015

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Michaela Vargová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/D4_Q1a: Sat 10. 10. 8:00–9:30 B1, 9:40–11:10 B1, 11:25–12:10 B1, Sat 21. 11. 8:00–9:30 B1, 9:40–11:10 B1, 11:25–12:55 B1, Sat 19. 12. 8:00–9:30 B1, 9:40–11:10 B1, D. Smetanová
MAT_1/D4_Q1b: Sat 7. 11. 8:00–9:30 B3, 9:40–11:10 B3, 11:25–12:55 B3, 13:05–14:35 B3, Sat 21. 11. 13:05–14:35 A2, 14:50–16:20 A2, 16:30–18:00 A2, 18:10–18:55 A2, D. Smetanová
MAT_1/P01: Tue 9:40–11:10 E1, D. Smetanová
MAT_1/P02: Tue 13:05–14:35 E1, D. Smetanová
MAT_1/S01: Wed 14:50–16:20 D515, J. Krieg
MAT_1/S04: Wed 9:40–11:10 D515, J. Vysoká
MAT_1/S05: Wed 11:25–12:55 D515, J. Krieg
MAT_1/S06: Tue 16:30–18:00 D616, M. Vacka
MAT_1/S07: Thu 9:40–11:10 B4, M. Vacka
MAT_1/S08: Thu 11:25–12:55 A5, M. Vacka
MAT_1/S09: Mon 11:25–12:55 A2, J. Vysoká
MAT_1/S10: Mon 13:05–14:35 A2, J. Vysoká
MAT_1/S11: Mon 14:50–16:20 A6, J. Vysoká
MAT_1/S12: Mon 8:00–9:30 A7, J. Vysoká
MAT_1/S13: Tue 8:00–9:30 A6, J. Vysoká
MAT_1/S14: Tue 9:40–11:10 A6, J. Vysoká
MAT_1/S15: Thu 13:05–14:35 D616, J. Vysoká
MAT_1/TP01: Tue 14:50–16:20 A219, M. Vargová
MAT_1/TS01: Tue 13:05–14:35 A219, M. Vargová

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2015

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Guaranteed by

RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/A2: Sat 7. 3. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:55 E1, Sat 18. 4. 13:50–14:35 E1, 14:50–16:20 E1, 16:30–18:00 E1, Sat 23. 5. 16:30–18:00 E1, 18:10–19:40 E1, D. Smetanová
MAT_1/P01: Wed 9:40–11:10 E1, D. Smetanová
MAT_1/P02: Wed 11:25–12:55 E1, D. Smetanová
MAT_1/S01: Wed 14:50–16:20 A5, D. Smetanová
MAT_1/S02: Mon 9:40–11:10 B3, M. Vargová
MAT_1/S03: Mon 16:30–18:00 B2, M. Vacka
MAT_1/S04: Tue 16:30–18:00 B3, J. Krieg
MAT_1/S05: Fri 11:25–12:55 A4, J. Vysoká
MAT_1/S06: Wed 14:50–16:20 B4, M. Vacka
MAT_1/S07: Wed 14:50–16:20 B5, M. Vargová
MAT_1/S08: Wed 16:30–18:00 B5, M. Vargová
MAT_1/S09: Fri 13:05–14:35 B4, J. Vysoká
MAT_1/S10: Fri 14:50–16:20 B4, J. Vysoká

Prerequisites

MAX_KOMBINOVANYCH(300) && MAX_PREZENCNICH(440)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2014

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Guaranteed by

RNDr. Dana Smetanová, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/D3: Sat 11. 10. 13:05–14:35 E1, 14:50–16:20 E1, Sun 2. 11. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:10 E1, Sat 22. 11. 11:25–12:55 E1, 13:05–14:35 E1, 14:50–16:20 E1, D. Smetanová
MAT_1/K11: Sat 11. 10. 13:05–14:35 E1, 14:50–16:20 E1, Sun 2. 11. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:10 E1, Sat 22. 11. 11:25–12:55 E1, 13:05–14:35 E1, 14:50–16:20 E1, D. Smetanová
MAT_1/P01: Tue 14:50–16:20 E1, D. Smetanová
MAT_1/P02: Tue 16:30–18:00 E1, D. Smetanová
MAT_1/P03: Wed 14:50–16:20 E1, D. Smetanová
MAT_1/S01: Wed 16:30–18:00 E4, D. Smetanová
MAT_1/S02: Wed 18:10–19:40 E4, D. Smetanová
MAT_1/S03: Tue 18:10–19:40 E4, D. Smetanová
MAT_1/S04: Tue 14:50–16:20 E5, M. Vargová
MAT_1/S05: Thu 9:40–11:10 B5, J. Krieg
MAT_1/S06: Fri 11:25–12:55 B3, J. Krieg
MAT_1/S07: Thu 8:00–9:30 A6, M. Vacka
MAT_1/S08: Thu 9:40–11:10 A6, M. Vacka
MAT_1/S09: Thu 11:25–12:55 A6, M. Vacka
MAT_1/S10: Fri 13:05–14:35 A4, M. Vacka
MAT_1/S11: Fri 9:40–11:10 D516, J. Vysoká
MAT_1/S12: Fri 11:25–12:55 D516, J. Vysoká
MAT_1/S13: Fri 13:05–14:35 D516, J. Vysoká
MAT_1/S14: Thu 11:25–12:55 A7, D. Smetanová
MAT_1/S15: Thu 13:05–14:35 A5, J. Vysoká
MAT_1/S16: Fri 8:00–9:30 D516, J. Vysoká
MAT_1/S17: Wed 13:05–14:35 D515, F. Šíma
MAT_1/TP01: Mon 9:50–11:20 A219, M. Vargová
MAT_1/TS01: Mon 11:40–13:10 A219, M. Vargová

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2014

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Petr Chládek, Ph.D. (lecturer)
doc. RNDr. Jaroslav Stuchlý, CSc. (lecturer)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Radek Vejmelka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jaroslav Krieg
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/A1: Sat 8. 3. 8:00–9:30 E1, 9:40–11:10 E1, 11:25–12:55 E1, Sat 5. 4. 14:50–16:20 E1, 16:30–18:00 E1, 18:10–18:55 E1, Sat 26. 4. 8:00–9:30 E1, 9:40–11:10 E1, D. Smetanová
MAT_1/P01: Fri 8:00–9:30 E1, J. Krieg
MAT_1/P02: Wed 8:00–9:30 E1, J. Krieg
MAT_1/S01: Fri 9:40–11:10 B5, M. Vacka
MAT_1/S02: Fri 9:40–11:10 B4, J. Krieg
MAT_1/S03: Thu 11:25–12:55 D515, J. Vysoká
MAT_1/S04: Thu 14:50–16:20 D515, M. Vacka
MAT_1/S05: Thu 16:30–18:00 D515, P. Chládek
MAT_1/S06: Thu 18:10–19:40 D515, P. Chládek
MAT_1/S07: Thu 9:40–11:10 D415, J. Krieg
MAT_1/S08: Fri 11:25–12:55 B5, J. Vysoká
MAT_1/S09: Fri 13:05–14:35 B5, J. Krieg
MAT_1/S10: Fri 14:50–16:20 B5, J. Krieg
MAT_1/S11: Fri 11:25–12:55 B4, D. Smetanová
MAT_1/S12: Fri 13:05–14:35 B4, D. Smetanová
MAT_1/S13: Fri 14:50–16:20 B4, D. Smetanová
MAT_1/S14: Mon 14:50–16:20 D415, P. Chládek
MAT_1/S15: Mon 13:05–14:35 B2, P. Chládek
MAT_1/S16: Wed 9:40–11:10 B4, M. Vacka

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2013

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
doc. RNDr. Jaroslav Stuchlý, CSc. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Radek Vejmelka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jaroslav Krieg
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/D2: Sat 12. 10. 12:46–13:30 B1, 13:40–15:10 B1, 15:15–16:45 B1, Sat 16. 11. 12:00–13:30 B1, 13:40–15:10 B1, Sat 7. 12. 8:00–9:30 B1, 9:40–11:10 B1, 12:00–13:30 B1, J. Krieg
MAT_1/K10_I: Sun 27. 10. 8:45–9:30 B2, 9:40–11:10 B2, 12:00–13:30 B2, Sat 16. 11. 8:00–9:30 B2, 9:40–11:10 B2, Sat 7. 12. 9:40–11:10 B2, 12:00–13:30 B2, 13:40–15:10 B2, J. Vysoká
MAT_1/K10_II: Sun 27. 10. 8:45–9:30 A2, 9:40–11:10 A2, 12:00–13:30 A2, Sat 16. 11. 8:00–9:30 A2, 9:40–11:10 A2, Sat 7. 12. 9:40–11:10 A2, 12:00–13:30 A2, 13:40–15:10 A2, D. Smetanová
MAT_1/P01: Mon 8:15–9:45 E1, J. Krieg
MAT_1/P02: Mon 9:55–11:25 E1, J. Krieg
MAT_1/S01: Mon 11:35–13:05 D516, D. Smetanová
MAT_1/S02: Mon 13:10–14:40 D416, D. Smetanová
MAT_1/S03: Mon 16:20–17:50 D616, D. Smetanová
MAT_1/S04: Mon 17:55–19:25 D516, D. Smetanová
MAT_1/S05: Tue 11:35–13:05 B5, J. Vysoká
MAT_1/S06: Tue 13:10–14:40 D616, J. Vysoká
MAT_1/S07: Tue 13:10–14:40 B5, J. Krieg
MAT_1/S08: Tue 16:20–17:50 B5, J. Vysoká
MAT_1/S09: Wed 9:55–11:25 D415, J. Krieg
MAT_1/S10: Wed 16:20–17:50 D616, J. Vysoká
MAT_1/S11: Thu 9:55–11:25 B2, J. Vysoká
MAT_1/S12: Thu 13:10–14:40 D616, J. Vysoká
MAT_1/S13: Thu 14:45–16:15 D616, J. Vysoká
MAT_1/S14: Fri 13:10–14:40 B4, J. Vysoká
MAT_1/S15: Fri 14:45–16:15 A6, J. Vysoká
MAT_1/S16: Mon 11:35–13:05 A2, J. Krieg
MAT_1/S17: Tue 14:45–16:15 A3, J. Vysoká

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	78
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	26
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2013

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Radek Vejmelka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jaroslav Krieg
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/CCV: Sat 16. 3. Sat 15:15–16:45 A4, Sat 16:50–18:20 A4, Sat 18:25–19:55 A4, Sun 14. 4. Sun 8:00–9:30 A4, Sun 9:40–11:10 A4, Sun 28. 4. Sun 16:00–16:45 A4, Sun 16:50–18:20 A4, Sun 18:25–19:55 A4, Sat 11. 5. Sat 14:45–16:15 A4, Sat 16:20–17:50 A4, Sat 17:55–19:25 A4, Sun 26. 5. Sun 13:10–14:40 A4, Sun 14:45–16:15 A4, Sun 16:20–17:05 A4, M. Vacka
MAT_1/E1: Sat 16. 3. 15:15–16:45 E1, 16:50–18:20 E1, 18:25–19:55 E1, Sun 14. 4. 8:00–9:30 E1, 9:40–11:10 E1, Sun 28. 4. 16:01–16:45 E1, 16:50–18:20 E1, 18:25–19:55 E1, J. Krieg
MAT_1/P01: Wed 13:10–14:40 E1, J. Krieg
MAT_1/P02: Tue 14:45–16:15 E1, J. Krieg
MAT_1/S01: Tue 9:55–11:25 A7, J. Vysoká
MAT_1/S02: Mon 9:55–11:25 D415, J. Krieg
MAT_1/S03: Thu 9:55–11:25 A2, J. Krieg
MAT_1/S04: Mon 11:35–13:05 A5, R. Vejmelka
MAT_1/S05: Wed 11:35–13:05 A2, J. Vysoká
MAT_1/S06: Fri 13:10–14:40 D616, J. Krieg
MAT_1/S07: Mon 14:45–16:15 A6, J. Vysoká
MAT_1/S08: Thu 14:45–16:15 D616, M. Vacka
MAT_1/S09: Wed 14:45–16:15 D616, J. Vysoká
MAT_1/S10: Fri 14:45–16:15 D616, J. Krieg
MAT_1/S11: Mon 16:20–17:50 A7, J. Vysoká
MAT_1/S12: Tue 17:55–19:25 D415, J. Krieg
MAT_1/S13: Wed 14:45–16:15 B2, J. Krieg
MAT_1/S14: Thu 11:35–13:05 A2, M. Vacka
MAT_1/S15: Fri 13:10–14:40 B5, M. Vacka

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Exam conditions

Exam-written: max. 120 points. Grading scale: F – less than 30 p., X – (30 - 59) p., E – (60 - 68) p., D – (69 - 76) p., C – (77 - 85) p., B – (86 - 94) p., A – 95 and more p..

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2012

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jaroslav Krieg
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/D1: Sat 20. 10. 15:15–16:45 B2, 16:50–18:20 B2, 18:25–19:55 B2, Sun 21. 10. 16:01–16:45 B1, 16:50–18:20 B1, 18:25–19:55 B1, Sun 9. 12. 16:50–18:20 B2, 18:25–19:55 B2, J. Krieg, Kombinovaná forma
MAT_1/K9: Sat 13. 10. 8:00–9:30 B2, 9:40–11:10 B2, Sun 4. 11. 15:15–16:45 B2, 16:50–18:20 B2, 18:25–19:10 B2, Sun 18. 11. 12:00–13:30 B2, 13:40–15:10 B2, 15:15–16:45 B2, J. Krieg, Kombinovaná forma
MAT_1/P01: Wed 13:10–14:40 E1, J. Krieg
MAT_1/S01: Tue 9:55–11:25 D516, P. Chládek
MAT_1/S02: Thu 8:15–9:45 B4, J. Vysoká
MAT_1/S03: Wed 14:45–16:15 D415, J. Vysoká
MAT_1/S04: Wed 16:20–17:50 B4, J. Krieg
MAT_1/S05: Wed 14:45–16:15 B3, J. Krieg
MAT_1/S06: Tue 8:15–9:45 D515, J. Krieg
MAT_1/S07: Thu 11:35–13:05 B4, J. Krieg
MAT_1/S08: Tue 11:35–13:05 D616, P. Chládek
MAT_1/S09: Thu 14:45–16:15 D616, J. Krieg
MAT_1/S10: Wed 9:55–11:25 D617, J. Vysoká

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Exam conditions

Exam-written: max. 120 points. Grading scale: F – less than 30 p., X – (30 - 59) p., E – (60 - 68) p., D – (69 - 76) p., C – (77 - 85) p., B – (86 - 94) p., A – 95 and more p..

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2012

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jaroslav Krieg
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/L1: Sat 17. 3. 15:15–16:45 B1, 16:50–18:20 B1, Sat 31. 3. 15:15–16:45 B1, 16:50–18:20 B1, 18:25–19:10 B1, Sun 15. 4. 8:00–9:30 B1, 9:40–11:10 B1, 12:00–13:30 B1, J. Vysoká, Kombinovaná forma
MAT_1/L2: Sat 10. 3. 8:00–9:30 B1, 9:40–11:10 B1, Sun 11. 3. 17:35–18:20 B1, 18:25–19:55 B1, Sun 29. 4. 16:50–18:20 B1, 18:25–19:55 B1, Sat 26. 5. 8:00–9:30 B1, 9:40–11:10 B1, M. Vacka, Kombinovaná forma
MAT_1/P01: Tue 8:15–9:45 B1, M. Vacka
MAT_1/P02: Tue 14:45–16:15 B1, M. Vacka
MAT_1/P03: Thu 9:55–11:25 B1, M. Vacka
MAT_1/S01: Tue 9:55–11:25 D617, F. Šíma
MAT_1/S02: Tue 8:15–9:45 D617, J. Vysoká
MAT_1/S03: Tue 9:55–11:25 A2, J. Vysoká
MAT_1/S04: Tue 11:35–13:05 A3, J. Vysoká
MAT_1/S05: Wed 8:15–9:45 D617, J. Vysoká
MAT_1/S06: Wed 9:55–11:25 A3, J. Vysoká
MAT_1/S07: Wed 11:35–13:05 A3, J. Vysoká
MAT_1/S08: Thu 8:15–9:45 D617, J. Vysoká
MAT_1/S09: Tue 16:20–17:50 A2, M. Vacka
MAT_1/S10: Fri 14:45–16:15 A4, D. Smetanová
MAT_1/S11: Fri 9:55–11:25 A2, D. Smetanová
MAT_1/S12: Fri 11:35–13:05 D617, D. Smetanová
MAT_1/S14: Thu 11:35–13:05 A3, J. Krieg
MAT_1/S15: Wed 11:35–13:05 A2, M. Vacka
MAT_1/S16: Tue 9:55–11:25 A3, J. Krieg
MAT_1/S17: Wed 8:15–9:45 A3, J. Krieg
MAT_1/S18: Tue 8:15–9:45 A3, J. Krieg

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Exam conditions

Exam-written: max. 120 points. Grading scale: F – less than 30 p., X – (30 - 59) p., E – (60 - 68) p., D – (69 - 76) p., C – (77 - 85) p., B – (86 - 94) p., A – 95 and more p..

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2011

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. František Šíma, Ph.D. (lecturer)
Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

Mgr. Petr Chládek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/ccv: Fri 30. 9. 13:50–17:55 D415, Sat 1. 10. 9:00–14:35 D415, Mon 3. 10. 8:15–9:00 B4, Tue 18. 10. 13:55–14:40 D111, J. Krieg, CCV studium
MAT_1/K8: Sat 22. 10. 13:40–15:10 B2, 15:15–16:45 B2, Sat 19. 11. 12:00–13:30 B2, 13:40–15:10 B2, 15:15–16:45 B2, 16:50–17:35 B2, Sat 3. 12. 8:00–9:30 B2, 9:40–11:10 B2, F. Šíma, Kombinovaná forma
MAT_1/L4: Sun 9. 10. 12:00–13:30 A4, 13:40–15:10 A4, Sun 13. 11. 16:01–16:45 A4, 16:50–18:20 A4, 18:25–19:55 A4, Sun 11. 12. 8:00–9:30 A4, Sat 7. 1. 8:00–9:30 A4, 9:40–11:10 A4, F. Šíma, Kombinovaná forma
MAT_1/P01: Tue 13:10–14:40 B1, P. Chládek
MAT_1/P02: Tue 8:15–9:45 A4, P. Chládek
MAT_1/S01: Mon 9:55–11:25 A6, J. Vysoká
MAT_1/S02: Mon 8:15–9:45 A6, J. Vysoká
MAT_1/S03: Wed 16:20–17:50 D415, J. Vysoká
MAT_1/S04: Mon 13:10–14:40 A2, J. Vysoká
MAT_1/S05: Thu 16:20–17:50 B2, P. Chládek
MAT_1/S06: Tue 11:35–13:05 A5, P. Chládek
MAT_1/S07: Wed 16:20–17:50 D516, F. Šíma
MAT_1/S08: Fri 11:35–13:05 D216, J. Krieg
MAT_1/S09: Fri 8:15–9:45 B4, M. Vacka

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

The content of the course are basic concepts of linear algebra and mathematical analysis (differential and integral calculus of functions of one variable).

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension vector space, scalar product of vectors. 2. Matrices, rank matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

Teacher's information

http://cantor.vstecb.cz/mediawiki/index.php/MATEMATIKA_1

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2011

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (lecturer)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Radek Vejmelka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Ing. Petra Bednářová, Ph.D. (assistant)

Guaranteed by

doc. RNDr. Jaroslav Stuchlý, CSc.
Department of Civil Engineering – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/ccv: Sat 16. 4. 8:15–9:45 D616, 9:55–11:25 D616, 12:10–13:40 D616, 13:50–15:20 D616, 15:30–17:00 D616, Sun 17. 4. 8:15–9:45 D616, 9:55–11:25 D616, 12:10–13:40 D616
MAT_1/KOPAK: Sat 16. 4. 8:15–9:45 A1, 9:55–11:25 A1, 12:10–13:40 A1, 13:50–15:20 A1, 15:30–17:00 A1, Sun 17. 4. 8:15–9:45 A1, 9:55–11:25 A1, 12:10–12:55 A1, J. Krieg
MAT_1/K7: Sun 6. 3. 12:10–13:40 A4, Sat 19. 3. 13:50–15:20 B4, Sun 20. 3. 12:10–13:40 A4, Sun 17. 4. 8:15–9:45 B4, 9:55–11:25 B4, Sat 23. 4. 8:15–9:45 B4, 9:55–11:25 B4, Sat 14. 5. 9:55–11:25 B1, M. Vacka
MAT_1/K8: Sat 19. 3. 15:30–17:00 B1, 17:10–18:40 B1, Sat 2. 4. 12:10–13:40 B1, Sun 1. 5. 8:15–9:45 B4, 9:55–11:25 B4, Sat 14. 5. 8:15–9:45 B1, Sun 22. 5. 12:10–13:40 B1, 13:50–14:35 B1, M. Vacka
MAT_1/01: Tue 14:25–15:55 Bazilika, M. Vacka
MAT_1/02: Wed 9:55–11:25 D515, J. Krieg
MAT_1/03: Wed 12:10–13:40 D616, J. Krieg
MAT_1/04: Wed 8:15–9:45 D617, J. Krieg
MAT_1/05: Thu 12:10–13:40 D516, F. Šíma
MAT_1/06: Wed 13:50–15:20 D515, F. Šíma
MAT_1/07: Thu 17:10–18:40 D616, F. Šíma
MAT_1/08: Wed 9:55–11:25 D516, F. Šíma
MAT_1/09: Wed 8:15–9:45 D415, F. Šíma
MAT_1/10: Wed 9:55–11:25 D416, M. Vacka

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

The content of the course are basic concepts of analytic geometry, linear algebra and mathematical analysis (differential calculus of functions of one variable).

Syllabus

Analytic geometry (line, plane, position, and metric problems) Vector, vector space, linear combinations of vectors, linear dependence of vectors, basis and dimension of vector space Matrices, matrix operations, matrix rank, the inverse matrix Solving linear equations, Gauss´s elimination Determinants, Cramer's rule Real Functions of One Real Variable Algebraic functions and nonalgebraic functions, inverse function Continuity of function(bilateral and unilateral continuity, discontinuity points), Limits of function (intrinsic or limits, limit of their points in half-point, levels of double-sided) Derivative of functions, differentiation rules, derivative of composite functions and implicit tangent function graph L´Hospital´s rule.Asymptotes of the graph feature. Graph Sketching

Literature

required literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

Teacher's information

http://cantor.vstecb.cz/mediawiki/index.php/MATEMATIKA_1

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
Winter 2010

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jaroslav Krieg (lecturer)
Mgr. Petr Janáček (seminar tutor)
RNDr. Petr Šebelík, CSc. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
Mgr. Radek Vejmelka (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jana Vysoká, Ph.D.
Department of Civil Engineering – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/K1: Mon 15. 11. 8:30–11:30 A4, Mon 29. 11. 8:30–11:30 A4, Mon 13. 12. 8:30–11:30 B4, Mon 3. 1. 8:30–11:30 A4, R. Vejmelka
MAT_1/K2: Mon 11. 10. 8:30–11:30 A4, Mon 25. 10. 8:30–11:30 A4, Mon 22. 11. 8:30–11:30 A4, Mon 20. 12. 8:30–11:30 A4, R. Vejmelka
MAT_1/K3: Sat 6. 11. 12:00–15:00 B1, Sun 7. 11. 12:45–16:30 Bazilika, Sun 5. 12. 8:30–11:30 B1, Sun 9. 1. 8:30–10:00 B1, R. Vejmelka
MAT_1/K4: Sun 7. 11. 12:45–16:30 Bazilika, Sun 21. 11. 12:00–15:00 A4, Sun 5. 12. 12:00–15:00 A4, Sun 19. 12. 12:00–15:00 A4, R. Vejmelka
MAT_1/K5: Sat 30. 10. 13:30–15:00 B1, Sun 7. 11. 12:45–13:30 Bazilika, 13:30–15:00 Bazilika, Sat 13. 11. 12:00–15:00 B1, Sat 27. 11. 8:30–11:30 B1, R. Vejmelka
MAT_1/K6: Sun 31. 10. 8:30–11:30 A4, Sun 7. 11. 12:45–16:30 Bazilika, Sat 13. 11. 8:30–11:30 A4, Sun 12. 12. 10:00–11:30 A4, R. Vejmelka
MAT_1/01: Mon 11:35–13:05 Bazilika, J. Krieg
MAT_1/02: Tue 11:10–12:40 Bazilika, J. Krieg
MAT_1/03: Thu 12:00–13:30 B3, R. Vejmelka
MAT_1/04: Wed 12:00–13:30 A3, R. Vejmelka
MAT_1/05: Tue 8:30–10:00 A2, P. Janáček
MAT_1/06: Tue 10:10–11:40 A2, P. Janáček
MAT_1/07: Wed 8:30–10:00 A6, R. Vejmelka
MAT_1/08: Wed 8:30–10:00 A5, J. Krieg
MAT_1/09: Wed 10:10–11:40 A5, J. Krieg
MAT_1/10: Wed 12:00–13:30 A5, J. Krieg
MAT_1/11: Wed 15:10–16:40 A5, J. Krieg
MAT_1/12: Wed 16:45–18:15 A5, J. Krieg
MAT_1/13: Thu 12:00–13:30 A4, J. Krieg
MAT_1/14: Thu 13:35–15:05 A4, J. Krieg
MAT_1/15: Thu 15:10–16:40 D416, J. Krieg
MAT_1/16: Thu 16:45–18:15 D416, J. Krieg
MAT_1/17: Mon 16:45–18:15 A3, M. Vacka
MAT_1/19: Tue 15:10–16:40 A2, M. Vacka
MAT_1/20: Wed 8:30–10:00 D616, J. Vysoká
MAT_1/21: Wed 10:10–11:40 A4, J. Vysoká
MAT_1/22: Thu 10:10–11:40 A1, J. Vysoká

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

The content of the course are basic concepts of linear algebra and mathematical analysis (differential calculus of functions of one variable).

Syllabus

Analytic geometry (line, plane, position, and metric problems)
Vector, vector space, linear combinations of vectors, linear dependence of vectors, basis and dimension of vector space
Matrices, matrix operations, matrix rank, the inverse matrix
Solving linear equations, Gauss´s elimination
Determinants, Cramer's rule
Real Functions of One Real Variable
Algebraic functions and nonalgebraic functions, inverse function
Continuity of function(bilateral and unilateral continuity, discontinuity points),
Limits of function (intrinsic or limits, limit of their points in half-point, levels of double-sided)
Derivative of functions, differentiation rules, derivative of composite functions and implicit tangent function graph
L´Hospital´s rule.Asymptotes of the graph feature
Asymptotes of graphs
Graph Sketching

Literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

Teacher's information

http://cantor.vstecb.cz/mediawiki/index.php/MATEMATIKA_1

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
Summer 2010

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Radek Vejmelka (lecturer)
PaedDr. Ing. Eva Blažková (seminar tutor)
Mgr. Alexander Sandany (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)

Guaranteed by

RNDr. Jana Vysoká, Ph.D.
Department of Civil Engineering – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/01: Mon 16:25–17:55 Bazilika, R. Vejmelka
MAT_1/02: Tue 11:25–12:55 Bazilika, R. Vejmelka
MAT_1/03: Tue 14:50–16:20 A6, R. Vejmelka
MAT_1/04: Thu 8:00–9:30 A2, R. Vejmelka
MAT_1/05: Thu 9:35–11:05 A2, R. Vejmelka
MAT_1/06: Wed 8:00–9:30 A6, R. Vejmelka
MAT_1/07: Wed 9:35–11:05 A6, R. Vejmelka
MAT_1/08: Wed 11:25–12:55 A6, R. Vejmelka
MAT_1/09: Mon 11:25–12:55 A3, R. Vejmelka
MAT_1/10: Mon 13:15–14:45 A3, R. Vejmelka
MAT_1/11: Mon 8:00–9:30 A2, E. Blažková
MAT_1/12: Mon 9:35–11:05 A2, E. Blažková
MAT_1/13: Mon 11:25–12:55 A2, E. Blažková
MAT_1/14: Mon 13:15–14:45 A2, E. Blažková
MAT_1/15: Thu 11:25–12:55 A5, F. Šíma
MAT_1/16: Thu 9:35–11:05 D516, F. Šíma
MAT_1/17: Thu 14:50–16:20 A6, M. Vacka
MAT_1/20: Wed 9:35–11:05 A2, M. Vacka
MAT_1/21: Wed 11:25–12:55 A2, M. Vacka
MAT_1/22: Wed 13:15–14:45 A2, M. Vacka

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Mathematics I deals with Linear Algebra and Calculus.

Syllabus

Analytic geometry
Vectors
Matrix algebra
Linear Systems of Equations
Determinant, Cramer's rule
Real Functions of One Real Variable
Basic functions
Continuity of function
Limits
Derivatives
L´Hospital´s rule
Asymptotes of graphs
Graph Sketching

Literature

Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught each semester.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
Winter 2009

Extent and Intensity

2/2. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Milan Vacka (lecturer)
RNDr. Jana Vysoká, Ph.D. (lecturer)
Mgr. Lucie Kubů (seminar tutor)
Mgr. Alexander Sandany (seminar tutor)
Mgr. František Šíma, Ph.D. (seminar tutor)
Mgr. Radek Trča (seminar tutor)

Guaranteed by

RNDr. Ing. Jana Kalová
Department of Civil Engineering – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

MAT_1/01: Mon 11:25–12:55 A4, J. Vysoká
MAT_1/02: Mon 13:15–14:45 A4, E. Blažková
MAT_1/03: Tue 8:00–9:30 A6, V. Kurcová
MAT_1/04: Tue 9:35–11:05 A6, V. Kurcová
MAT_1/05: Tue 11:25–12:55 A6, V. Kurcová
MAT_1/06: Tue 13:15–14:45 A6, V. Kurcová
MAT_1/07: Tue 14:50–16:20 A6, J. Vysoká
MAT_1/08: Tue 16:25–17:55 A6, J. Vysoká
MAT_1/09: Tue 18:15–19:45 A6, J. Vysoká
MAT_1/10: Wed 9:35–11:05 A2, A. Sandany
MAT_1/11: Thu 8:00–9:30 A4, L. Kubů
MAT_1/12: Thu 9:35–11:05 E7, L. Kubů
MAT_1/13: Thu 13:15–14:45 B5, F. Šíma
MAT_1/14: Thu 14:50–16:20 B5, A. Sandany
MAT_1/15: Thu 16:25–17:55 B5, A. Sandany
MAT_1/16: Thu 18:15–19:45 B5, A. Sandany
MAT_1/17: Thu 8:00–9:30 B4, R. Trča
MAT_1/18: Thu 9:35–11:05 B4, R. Trča
MAT_1/19: Thu 11:25–12:55 B4, R. Trča
MAT_1/20: Thu 13:15–14:45 B4, V. Kurcová
MAT_1/21: Thu 14:50–16:20 B4, V. Kurcová
MAT_1/22: Thu 16:25–17:55 B4, V. Kurcová
MAT_1/23: Thu 18:15–19:45 B4, V. Kurcová
MAT_1/24: Thu 11:25–12:55 D517, L. Kubů
MAT_1/25: Mon 14:00–15:30 P1, J. Vysoká
MAT_1/26: Tue 8:00–9:30 A1, M. Vacka
MAT_1/27: Tue 9:35–11:05 A1, M. Vacka
MAT_1/28: Tue 11:25–12:55 A1, J. Vysoká
MAT_1/29: Wed 7:30–9:00 P1, J. Vysoká
MAT_1/30: Wed 9:05–10:35 P1, J. Vysoká

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Mathematics I deals with Linear Algebra and Calculus.

Syllabus

1. Linear Algebra 2. Vectors 3. Matrix Algebra 4. Determinant 5. Linear Systems of Equations 6. Least Squares 7. Real Functions of One Real Variable 8. Basic Notions 9. Limits and Continuity 10. Derivatives 11. L´Hospital´s rule 12. Asymptotes of graphs 13. Graph Sketching

Literature

Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Follow-Up Courses

MTT_2 Mathematics II (Civil engineering)

Further Comments

The course is taught each semester.

Teacher's information

http://cantor.vstecb.cz

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
Summer 2009

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Ing. Jana Kalová (lecturer)
prof. Pavel Kindlmann, DrSc. (seminar tutor)

Guaranteed by

Institute of Technology and Business in České Budějovice

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes (in Czech)

Název studijního předmětu Matematika 1 Obor / kód předmětu EP, SM / MAT 1 Typ předmětu povinný Doporuč. ročník / semestr 1 / 1 Počet kreditů 5 Rozsah studijního předmětu přednáška 2 P seminář 2 S Způsob zakončení zkouška ano zápočet ano Podmínky o podmínkou získání zápočtu je průběžné plnění úkolů a úspěšné napsání zápočtového testu o podmínky pro úspěšné složení zkoušky budou oznámeny na začátku semestru Stručná anotace předmětu Obsahem předmětu jsou základní pojmy lineární algebry a matematické analýzy (diferenciální počet funkce jedné reálné proměnné). Tematické okruhy přednášek o Analytická geometrie v prostoru (přímka, rovina, polohové a metrické úlohy) o Vektor, vektorový prostor, lineární kombinace vektorů, lineární závislost a nezávislost vektorů, báze a dimenze vektorového prostoru o Matice, operace s maticemi, hodnost matice, inverzní matice o Řešení soustav lineárních rovnic, Gaussova eliminace o Determinanty, Cramerovo pravidlo o Funkce jedné reálné proměnné - definice a základní vlastnosti o Funkce algebraické a nealgebraické, funkce inverzní o Spojitost funkce (oboustranná a jednostranná spojitost, body nespojitosti) o Limita funkce (vlastní a nevlastní limita, limita ve vlastních bodech, v nevlastních bodech, limity oboustranné, jednostranné) o Derivace funkce, základní pravidla pro derivování, derivace funkce složené a implicitně zadané, tečna grafu funkce o L´Hospitalovo pravidlo o Vyšetřování průběhu funkce užitím diferenciálního počtu. Asymptoty grafu funkce. o Diferenciál funkce a jeho užití. Studijní literatura Povinná literatura: KAŇKA, M., COUFAL, J., KLŮFA, J.: Učebnice mat

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught each semester.
The course is taught: every week.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics 1

Institute of Technology and Business in České Budějovice
Winter 2008

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Ing. Jana Kalová (lecturer)
prof. Pavel Kindlmann, DrSc. (seminar tutor)

Guaranteed by

Institute of Technology and Business in České Budějovice

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes (in Czech)

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught each semester.
The course is taught: every week.

The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Matematika I

Institute of Technology and Business in České Budějovice
Summer 2008

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jana Vysoká, Ph.D.

Guaranteed by

Institute of Technology and Business in České Budějovice

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes (in Czech)

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught each semester.
The course is taught: every week.

The course is also listed under the following terms Summer 2007, Winter 2007, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics 1

Institute of Technology and Business in České Budějovice
Winter 2007

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Ing. Jana Kalová
Mgr. Michaela Petrová
RNDr. Jana Vysoká, Ph.D.

Guaranteed by

Institute of Technology and Business in České Budějovice

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes (in Czech)

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught each semester.
The course is taught: every week.

The course is also listed under the following terms Summer 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics 1

Institute of Technology and Business in České Budějovice
Summer 2007

Extent and Intensity

0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Jana Vysoká, Ph.D. (lecturer)
Mgr. Michaela Petrová (seminar tutor)

Guaranteed by

Institute of Technology and Business in České Budějovice

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes (in Czech)

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	52	115
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – oral 5 %
Exam – written 95 %

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.
The course is taught each semester.
The course is taught: every week.

The course is also listed under the following terms Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, summer 2018, winter 2018, summer 2019, winter 2019, winter 2020.

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2024

The course is not taught in winter 2024

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	67
Preparation for the Final Test	20	26
Semester project	20	20
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Presentation	2	2
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.
General note: Exitus.

Teacher's information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2023

The course is not taught in winter 2023

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	67
Preparation for the Final Test	20	26
Semester project	20	20
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Presentation	2	2
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.
General note: Exitus.

Teacher's information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2022

The course is not taught in winter 2022

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	67
Preparation for the Final Test	20	26
Semester project	20	20
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Presentation	2	2
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.
General note: Exitus.

Teacher's information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2021

The course is not taught in winter 2021

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)

Guaranteed by

Prerequisites

The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Exercise
Tutorial
Consultation

Teaching Methods

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	67
Preparation for the Final Test	20	26
Semester project	20	20
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Presentation	2	2
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points.

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.
General note: Exitus.

Teacher's information

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2021

The course is not taught in summer 2021

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (lecturer)

Guaranteed by

Prerequisites

OBOR(CAP)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8

recommended literature

Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	89
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.

Teacher's information

https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf

MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2020

The course is not taught in summer 2020

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Mgr. Petr Chládek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)

Guaranteed by

Ing. Lukáš Polanecký
Lifelong learning Centre – Directorate of Study Administration and Lifelong Learning – Vice-Rector for Study Affairs – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Prerequisites

OBOR(CAP)
The student masters the range of secondary school mathematics or the ZAM course.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

Learning outcomes

Syllabus

1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.

Literature

required literature

DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.

recommended literature

MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. In Expert. 2. vyd. Praha: Grada, 2015
Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. info

Forms of Teaching

Lecture
Seminar
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
Activities	Daily Study	Combined Study
Preparation for Lectures	26
Preparation for Seminars, Exercises, Tutorial	26	89
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	15
Total:	130	130

Assessment Methods and Assesment Rate

Exam – written 70 %
activity during seminar 30 %

Exam conditions

Language of instruction

Czech

Follow-Up Courses

Further comments (probably available only in Czech)

The course is taught each semester.
The course is taught: every week.

Teacher's information

Enrolment Statistics (recent)

Course Information

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics 1

MAT_1 Matematika I

MAT_1 Mathematics 1

MAT_1 Mathematics 1

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

MAT_1 Mathematics I

Other applications