Calculus B2

Course guarantor:

Lecturer:

Tutor:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: