Course detail

Mathematics 2

FP-MA2_MAcad. year: 2024/2025

This course follows Mathematics I course. Content is linear algebra, differential calculus of several variables, differential and difference equations (mainly linear) and instruments for their only solution - power series and Fourier series and selected integral transformation.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Knowledge of secondary-school mathematics and successful completion of the course “Mathematics I”.

Rules for evaluation and completion of the course

Conditions for awarding course-unit credits:
-active participation in the seminars where the attendance is compulsory,
-fulfilment of individual tasks and successful completion of written assignments,
-working out of a semester project marked with at least “E”,
-completion of partial written exams marked more than 55% points

The exam has a written and an oral part with the written part being more important.

 

Attendance at exercises (seminars) is controlled.

Aims

The aim of the course is to build up mathematical tools necessary for the instruction of specialized courses.
Acquired knowledge and practical mathematical skills will be an important starting point for mastering new knowledge in the follow-up courses of mathematical character; they will also be essential for acquiring knowledge in courses on economy and for the correct use of mathematical software.

Study aids

Viz. literature

Prerequisites and corequisites

Not applicable.

Basic literature

Mezník, I: Diskrétní matematika. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno, Brno 2004. ISBN 80-214-2754-X. (CS) (CS)
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS)
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

1. Course of function I (monotonicity, local and absolute extrema of the function)
2. Course of the function II (convexity and concavity; asymptotes of the function, complete description of the behavior of the function)
3. Indefinite integral (meaning, properties, basic rules for calculation)
4. Integration methods I (per partes and substitution method)
5. Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
6. Definite integral (meaning, properties, calculation rules, applications, improper integral)
7. Summary (function progression, function integral)
8. Differential equation of the 1st order (with separated variables, linear)
9. Linear differential equation of the 2nd order (with constant coefficients)
10. Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
11. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
12. Summary (definite integral, differential equation, introduction to functions of several variables)
13. Bound extrema (Lagrange method)

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

1. Differential and derivatives of higher orders (differential and its use, derivatives of higher orders, l'Hospital's rule)
2. Course of function I (monotonicity, local and absolute extrema of the function)
3. Course of the function II (convexity and concavity; asymptotes of the function, complete description of the behavior of the function)
4. Indefinite integral (meaning, properties, basic rules for calculation)
5. Integration methods I (per partes and substitution method)
6. Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
7. Definite integral (meaning, properties, rules for calculation)
8. Definite integral (application)
9. Differential equation of the 1st order (with separated variables, linear)
10. Linear differential equation of the 2nd order (with constant coefficients)
11. Functions of multiple variables and partial derivatives (graph and its sections, partial derivatives, differential)
12. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
13. Extrema of functions of several variables