VŠTE:MAT_a Mathematics - Course Information

MAT_a Mathematics

Extent and Intensity

2/2/0. 5 credit(s). Type of Completion: zk (examination).

Guaranteed by

RNDr. Jana Vysoká, 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

Course Enrolment Limitations

The course is offered to students of any study field.

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
• DELVENTHAL, K. M. et al., 2017. Kompendium matematiky. Praha: [s. n.]. ISBN 978-80-242-5420-3.
• BEEZER, R. A., 2015. A First Course in Linear Algebra. 3rd edit. [s. l.]: Congruent Press. ISBN 978-0984417551.
• MOUČKA, J. a P. RÁDL, 2015. Matematika pro studenty ekonomie. 2. uprav. a dopl. vyd. Praha: Grada. ISBN 978-80-247-5406-2.
• 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.

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

Activities	Number of Hours of Study Workload
	Daily Study	Combined Study
Preparation for the Mid-term Test	14
Preparation for Lectures	18
Preparation for Seminars, Exercises, Tutorial	18	86
Preparation for the Final Test	26	26
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	26	16
Presentation	2	2
Total:	130	130

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. If the attendance is not fulfilled, the student will be automatically classified as “F”.

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). 70% attendance is obligatory for full-time students.

• Enrolment Statistics (summer 2021, recent)
  
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