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
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
  • 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. 298 s. ISBN 978-80-86929-53-8. 2009. Obsah info
  • KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress. 222 s. ISBN 80-86119-76-9. 2003. info
  • DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment. 460 s. ISBN 80-7200-587-1. 2003. 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, Tutorial52115
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2615
Total:130130
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.
  • Enrolment Statistics (summer 2012, recent)
  • Permalink: https://is.vstecb.cz/course/vste/summer2012/MAT_1