B_MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
winter 2025
Extent and Intensity
2/4/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
RNDr. Jaroslav Krieg (seminar tutor)
Mgr. Daniel Lašan (seminar tutor)
Ing. Květa Papoušková, Ph.D. (seminar tutor)
RNDr. Dana Smetanová, 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_1/K08: Sat 27. 9. 13:05–14:35 E1, Sun 19. 10. 8:00–12:30 E1, Sat 8. 11. 8:00–12:30 E1, Sun 23. 11. 8:00–12:30 E1, Sun 21. 12. 13:05–16:05 E1, D. Smetanová
B_MAT_1/P01: Mon 13:05–14:35 E1, Z. Dušek
B_MAT_1/S01: Thu 13:05–14:35 E1, Fri 9:40–11:10 B2, D. Lašan
B_MAT_1/S02: Wed 8:00–9:30 B3, Thu 9:40–11:10 B3, K. Papoušková
B_MAT_1/S03: Tue 14:50–16:20 B3, Fri 13:05–14:35 B3, D. Lašan
B_MAT_1/S04: Tue 13:05–14:35 B2, Wed 13:05–14:35 B2, J. Krieg
B_MAT_1/S05: Wed 11:25–12:55 B3, Thu 13:05–14:35 D516, J. Krieg
B_MAT_1/S06: Tue 14:50–16:20 E1, Thu 14:50–16:20 B3, J. Krieg
B_MAT_1/S07: Wed 9:40–11:10 B3, Thu 8:00–9:30 B3, K. Papoušková
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, operations with vectors, linear dependence and independence of vectors, bases and dimensions of vector space 2. Matrices, operations with matrices, Gaussian elimination method 3. Systems of linear equations, Frobeni's theorem 4. Inverse matrix, matrix equation 5. Determinants, Cramer's rule 6. Functions of one real variable and its properties 7. Function limit 8. Derivation of a function and its geometric meaning, rules for derivation 9. L´Hospital's rule. Significance of the 1st derivative for the course of a function (increasing, decreasing functions) 10. Significance of the 2nd derivative for the course of the function (convex, concave, local extrema and inflection points), asymptotes of the function 11. Primitive functions, indefinite integral, direct integration 12. Method of per-partes integration 13. Substitution method
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
  • MUSILOVÁ J., MUSILOVÁ P., 2012. Matematika II/2 pro porozumění a praxi: netradiční výklad tradičních témat vysokoškolské matematiky. Brno: VUTIUM. ISBN: 978-80-214-4071-5.
  • CHLÁDEK P., 2012. Matematika I. České Budějovice: Vysoká škola technická a ekonomická v Českých Budějovicích. ISBN 978-80-7468-004-5.
  • KAŇKA, M., 2009. Sbírka řešených příkladů z matematiky: pro studenty vysokých škol. 1. Vydání. Praha: Ekopress, 298 s. ISBN 978-80-86929-53-8.
  • MOUČKA, J., RÁDL, P., 2015. Matematika pro studenty ekonomie. 2., 1. Vydání. Praha: Grada Publishing. Expert. 272 stran. ISBN 978-80-247-5406-2.
  • MUSILOVÁ J., MUSILOVÁ P., 2012. Matematika II/1 pro porozumění a praxi: netradiční výklad tradičních témat vysokoškolské matematiky. Brno: VUTIUM. ISBN: 978-80-214-4071-5.
  • MUSILOVÁ J., MUSILOVÁ P., 2009. Matematika I pro porozumění i praxi: netradiční výklad tradičních témat vysokoškolské matematiky, Brno: VUTIUM. ISBN: 978-80-214-3631-2.
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
E-learning
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for the Mid-term Test20 
Preparation for Lectures4 
Preparation for Seminars, Exercises, Tutorial44120
Preparation for the Final Test3434
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion5226
Participation in the final test22
Total:182182
Assessment Methods and Assesment Rate
Test – mid-term 30 %
Test – final 70 %
Exam conditions
Full-time form - test max 70 points (+ max 30 points continuous assessment), combined form - test 100 points. Overall classification of the course, ie points for the final evaluation (70 - 0) + points from the continuous evaluation (30 - 0): Z 100 - 70, X 69.99 - 30, N 29.99 - 0. The student of the full-time form of study is obliged to fulfill the obligatory 70% attendance at the contact teaching, ie everything except lectures. If the participation is not met, the student will be automatically classified "-".
Language of instruction
Czech
Follow-Up Courses
Teacher's information
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.
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