VŠTE:MAT_1 Mathematics I - Course Information

MAT_1 Mathematics I

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

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
	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

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

• MAT_2 Mathematics_2
• MAT_3 Mathematics III

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

• Enrolment Statistics (winter 2015, recent)
  
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