B_MAT Mathematics

Institute of Technology and Business in České Budějovice
winter 2025
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Ing. Bc. Karel Antoš, Ph.D. (seminar tutor)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Mgr. Daniel Lašan (seminar tutor)
Ing. Květa Papoušková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, 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
B_MAT/K08: Sat 4. 10. 14:50–16:20 E1, Sun 2. 11. 13:05–17:35 E1, Sun 16. 11. 13:05–17:35 E1, Sat 20. 12. 11:25–12:55 E1, K. Papoušková
B_MAT/P01: Thu 11:25–12:55 E1, Z. Dušek
B_MAT/S01: Tue 8:00–9:30 B3, K. Papoušková
B_MAT/S02: Tue 13:05–14:35 B3, K. Papoušková
B_MAT/S03: Mon 13:05–14:35 B2, K. Papoušková
B_MAT/S04: Thu 14:50–16:20 B2, D. Lašan
B_MAT/S05: Fri 11:25–12:55 B2, D. Lašan
B_MAT/S06: Fri 13:05–14:35 I317A, K. Papoušková
B_MAT/S07: Wed 18:10–19:40 E1, D. Lašan
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives supported by learning outcomes
Learning outcomes of the course unit The aim of the course is to provide students with basic knowledge of linear algebra, differential and integral calculus of the function of one real variable needed in the study of specialized subjects and to present and explain the key methods and algorithms.
Learning outcomes
Upon successful completion of this course, the student: 1. Solve basic tasks from the subject matter 2. is familiar with the concepts of higher mathematics and the suitability of their use 3. applies knowledge to specialized subjects 4. uses basic procedures for practical tasks 5. understands the wider context and strategic role of mathematics in practice
Syllabus
Lectures 1. Vector, vector space, equality of vectors, counting with vectors, linear combination of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrix, addition and multiplication of matrices, inverse matrix, Frobenius theorem, solving systems of linear equations by Gaussian method. 3. Determinants, Cramer rule. 4. Functions of one real variable, domain and range of functional values, basic algebraic and non-algebraic functions. 5. Inverse function, even and odd function, cyclometric function. 6. Limit of function. 7. Derivative of a function, basic rules for differentiation, derivative of a composite function, tangent of a function graph. 8. L´Hospital rule. Significance of the 1st and 2nd derivative for the function (increasing, decreasing, convex, concave, local extremes and inflection points). 9. Primitive function, indefinite integral, direct integration. 10. Per-partes integration method. 11. Substitution method. 12. Definite integral. 13. Calculation of planar pattern. Seminars 1. Vector calculus, linear dependence and independence of vectors. 2. Matrix calculus, Gaussian elimination method for solving systems of linear equations. 3. Calculation of determinants of a square matrix and Cramer rule for systems of linear equations. 4. Properties of functions of one real variable. 5. Calculation of inverse functions, even and odd functions. 6. Calculation of selected types of function limits. 7. Derivation of sum, difference, product, ratio and compound function. 8. Using L´Hospital rule for calculating function limits. Calculation of intervals at which the function is increasing, decreasing, convex, concave, and calculation of local extremes, inflection points. 9. Calculation using direct function integration. 10. Calculation of indefinite integrals by the per-partes method. 11. Calculation of indefinite integrals by the substitution method. 12. Calculation of definite integral, Newton-Leibnitz formula. 13. Simple applications of indefinite integral.
Literature
    required literature
  • BEEZER, R. A., 2015. A First Course in Linear Algebra. 3rd edit. [s. l.]: Congruent Press. ISBN 978-0984417551.
  • DELVENTHAL, K. M. et al., 2017. Kompendium matematiky. Praha: [s. n.]. ISBN 978-80-242-5420-3.
  • KLŮFA, J., 2016. Matematika pro Vysokou školu ekonomickou. Praha: Ekopress. ISBN 978-80-87865-32-3.
  • STRANG, G. a E. HERMAN, 2016. Calculus Volume 1. [s. l.]: [s. n.]. ISBN 978-1938168024.
  • MOUČKA, J. a P. RÁDL, 2015. Matematika pro studenty ekonomie. 2. uprav. a dopl. vyd. Praha: Grada. ISBN 978-80-247-5406-2.
    recommended literature
  • DOŠLÁ, Z. a P. LIŠKA, 2014. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. Praha: Grada. ISBN 978-80-247-5322-5.
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
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test14 
Preparation for Lectures18 
Preparation for Seminars, Exercises, Tutorial1886
Preparation for the Final Test2626
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2616
Presentation22
Total:130130
Assessment Methods and Assesment Rate
Test – mid-term 30 %
Test – final 70 %
Combined form - final test for 100 b 100 %
Exam conditions
Full-time form: Continuous tests (total 30 p), Final test (total 70 p) Combined form: Final test (total per 100 p) For successful completion of the course it is necessary to achieve at least 70% of the total and final evaluation under the conditions set out below. In the interim evaluation it is possible to get 30 points, ie 30%. In the final evaluation you can get a total of 70 points, ie 70%. Overall classification of the course, ie points for final evaluation (70 - 0) + points from continuous evaluation (30 - 0): 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. Full-time students are obliged to fulfill the compulsory 70% attendance at contact instruction, ie everything except lectures.
Language of instruction
Czech
Teacher's information
Participation in all forms of education is solved by a separate internal standard of VŠTE (Evidence of students' attendance at VŠTE).
  • Enrolment Statistics (recent)
  • Permalink: https://is.vstecb.cz/course/vste/winter2025/B_MAT