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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Calculus B2

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Code Completion Credits Range Language
01MAB2 Z,ZK 7 2+4 Czech
Grading of the course requires grading of the following courses:
Calculus 1 (01MA1)
Lecturer:
Severin Pošta (guarantor)
Tutor:
Severin Pošta (guarantor), Jiří Fejlek, Petr Gális, Hanka Řada, Jana Vacková, Aleš Wodecki
Supervisor:
Department of Mathematics
Synopsis:

Basic calculus (real analysis, indefinite and definite integrals and series).

Requirements:

Calculus 1 (01MANA or 01MANB).

Syllabus of lectures:

1. Antiderivative - basic properties, integration by parts, by substitution, antiderivative of rational and other elementary functions.

2. Newton and Riemann integrals, their relation, convergence of integral.

3. Some applications of integral - area of plane regions, length of a curve, volume and surface areas.

4. Infinite series - sum, basic properties, convergence of series with nonnegative terms, with arbitrary terms.

Syllabus of tutorials:

1. Antiderivatives. Integration by parts, by substitution.

2. Calculus of Riemann integrals.

3. Applications of integrals.

4. Infinite series and their convergence.

Study Objective:

The goal of this course is to manage basic techniques of computing indefinite and definite integrals and examining convergence of sequences.

Study materials:

Recommended references:

[1] T. Apostol: Mathematical Analysis, Addison Wesley, 1974.

[2] W. Rudin: Principles of Mathematical Analysis. McGraw-Hill, Mexico, 1980.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-10-17
For updated information see http://bilakniha.cvut.cz/en/predmet10379405.html