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
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/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
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.
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
  • 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
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Lectures26 
Preparation for Seminars, Exercises, Tutorial2689
Preparation for the Final Test2626
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2615
Total:130130
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
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 2020.
  • Enrolment Statistics (winter 2019, recent)
  • Permalink: https://is.vstecb.cz/course/vste/winter2019/MAT_1