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
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Lectures26 
Preparation for Seminars, Exercises, Tutorial52115
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2615
Total:130130
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.
  • Enrolment Statistics (winter 2011, recent)
  • Permalink: https://is.vstecb.cz/course/vste/winter2011/MAT_1