Mathematical Analysis A 3

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Function sequences and series, introduction to topology and metric spaces, differential calculus of functions of several variables.

Requirements:

Mathematical analysis and linear algebra on the level of the first year courses at FNSPE.

Syllabus of lectures:

1. Function sequences and series: pointwise and uniform convergence, interchange conditions for limits, derivatives and

integrals, power and Taylor series, trigonometric and Fourier series.

2. Topology and metric spaces: basic notions, continuity, compact, connected and complete spaces.

3. Differential calculus of function of several variables: derivative, directional and partial derivatives, derivatives of higher order, mean-value theorems,

extrema of functions of several variables.

Syllabus of tutorials:

0. Repetition: Convergence of the Riemann integral.

1. Uniform convergence of function sequences and series.

2. Fourier series.

3. Topology.

4. Derivative, differentiability.

5. Extrema of functions of several variables.

Study Objective:

Study materials:

Literature:

[1] Chp. 1-3. in Czech lecture note „F. Štampach: Matematická analýza A3 a A4“ available at http://stampach.xyz/fjfi_stud.html

Further recommended literature:

[2] W. Rudin: Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.

[3] B. P. Demidovich: Problems in mathematical analysis. Translated from the Russian by G. Yankovsky. Third printing. Mir Publishers, Moscow, 1973.

[4] G. B. Folland: Real Analysis: Modern Techniques and Their Applications, 2nd edition, A Willey-Interscience Publication, 1999.

[5] G. B. Folland: Advanced calculus, Pearson, 2001.

[6] M. Moskowitz, F. Paliogiannis: Functions of several real variables, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: