Course detail

# Mathematical Analysis 2

Series. The Fourier an wavelet transforms. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

Learning outcomes of the course unit

The ability to understand the basic problems of higher calculus
and use derivatives, integrals and differential equations for solving specific problems.

Prerequisites

The IMA1 course.

• recommended prerequisite

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Written tests during semester (maximum 30 points).
Exam prerequisites:
At least 10 points from the tests during the semester.

Language of instruction

Czech, English

Work placements

Not applicable.

Aims

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles
and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems.

Specification of controlled education, way of implementation and compensation for absences

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Number series.
2. Power series.
3. Fourier series.
4. Fourier transform, discrete Fourier transform.
5. Wavelets, wavelet transform.
6. Functions of several variables (particularly in 2 and 3 dimensions), limit and continuity.
7. Differential calculus of functions of several variables I: partial derivatives, Hess matrix, Schwarz theorem.
8. Differential calculus of functions of more variables II: local extrema, Sylvester criterion.
9. Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
10. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
11. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
12. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equations.
13. Numerical solution of differential equations of the first order.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer

eLearning