VŠTE:MAT Mathematics - Course Information

MAT Mathematics

Extent and Intensity

0/4/0. 4 credit(s). Type of Completion: zk (examination).

Teacher(s)

RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Milan Vacka (seminar tutor)
RNDr. Jana Vysoká, 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

MAT/X01: Sun 11. 10. 8:00–9:30 D416, 9:40–11:10 D416, 11:25–12:55 D416, Sat 7. 11. 8:00–9:30 E5, 9:40–11:10 E5, 11:25–12:55 E5, Sat 28. 11. 8:00–9:30 E5, 9:40–11:10 E5, Sun 13. 12. 8:00–9:30 E5, 9:40–11:10 E5, D. Smetanová
MAT/SX01: Mon 11:25–12:55 N109, Fri 11:25–12:55 N109, J. Vysoká
MAT/SX02: Mon 13:05–14:35 N109, Fri 13:05–14:35 N109, D. Smetanová
MAT/SX03: Mon 11:25–12:55 N109, Fri 11:25–12:55 N109, J. Vysoká

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.

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
• MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. 2., uprav. a dopl. vyd. Praha: Grada Publishing, 2015. Expert (Grada). ISBN 978-80-247-5406-2.
• CHLÁDEK, Petr. Matematika I : studijní opora pro kombinované studium. 1. vyd. České Budějovice: Vysoká škola technická a ekonomická v Českých Budějovicích, 2012, 44 pp. ISBN 978-80-7468-004-5. info

recommended literature
• MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika I : pro porozumění i praxi : netradiční výklad tradičních témat vysokoškolské matematiky. 2., dopl. vyd. Brno: VUTIUM, 2009, 339 pp. ISBN 978-80-214-3631-2. Obsah info
• 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
• KAŇKA, Miloš. Vybrané partie z matematiky pro ekonomy. Vyd. 1. Praha: Vysoká škola ekonomická, Fakulta informatiky a statistiky, 1998, 231 s. ISBN 80-7079-537-9. info

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

Activities	Number of Hours of Study Workload
	Daily Study	Combined Study
Presentation	6	6
Preparation for the Mid-term Test	14	13
Preparation for Seminars, Exercises, Tutorial	18	13
Preparation for the Final Test	20	20
Semester project	20	20
Attendance on Seminars/Exercises/Tutorial/Excursion	26	32
Total:	104	104

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

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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