Course detail

Infinite series and their applications

FAST-5A0Acad. year: 2018/2019

Sequences and series with constant terms, convergence criteria, absolute and relative convergence, alternating series, functional series, pointwise and uniform convergence, derivation and integration term by term, power series, approximation of definite integrals, solution of selected types od ordinary differential equations.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

RNDr. Oldřich Dlouhý

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

Prerequisites

The subjects taught in the 0A1 course.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Sequences, number series, sums of numbers series.
2. Convergent and divergent series. Special number series.
3. Convergence criteria of number series with positive terms.
4. Absolute and relative convergence of alternating series.
5. Approximate calculation of the sum of a series.
6. Calculation with series.
7. Functional series, point convergence, domain of convergence of a functional series.
8. Uniform convergence, derivative and integral of series term by term.
9. Power series, basic properties, domains of convergence.
10.Derivative and integral of a power series, sum of a power series.
11. Using power series to calculate integrals.
12. Using power series to solve selected differential equations.
13.- 14. Solving problems

Work placements

Not applicable.

Aims

Since the academic year 2004/2005 this course is no longer offered as optional.

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ŠKRÁŠEK, TICHÝ: Základy aplikované matematiky II. SNTL Praha 1986
VEVERKA. J.: Matematika II3 (Nekonečné řady). CERM Brno 1998

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Oldřich Dlouhý