Calculus 1

Lecturer:

Severin Pošta (gar.)

Tutor:

Severin Pošta (gar.), Petr Ambrož, Lubomíra Balková, Ondřej Glatz, Jitka Hanousková, Martin Heller, Jiří Mikyška, Edita Pelantová, Barbora Planková, Jiří Pytlíček, Josef Schmidt, Jan Starý, Jan Tláskal, Petr Veverka, Miroslav Zima

Supervisor:

Department of Mathematics

Synopsis:

Basic course of real analysis (functions of one real variable, differential calculus).

Requirements:

No prerequisities.

Syllabus of lectures:

1. Basics of mathematical logic, equations and inequalities, goniometric functions, exponential and logarithmic functions, sums and products, induction. 2. Sets and mappings. 3. Real and complex sequence - limit, basic properties, limits of special sequences, number „e“ and exponential function, some elementary functions. 4. Limit and continuity of functions of one real variable - basic properties. 5. Derivative of functions - basic properties. 6. Basic theorems of differential calculus. 7. Constructing graph of functions.

Syllabus of tutorials:

1. Basic properties of functions and mappings. 2. Supremum, Infimum. 3. Limits of sequences. 4. Acculumation points. 5. Limits of real functions. 6. Continuity. 7. Derivative, graphs of real functions.

Study Objective:

The goal of this course is to manage basic techniques of computing limits of sequences, limits of real functions of one real variable and of differential calculus.

Study materials:

Apostol: Mathematical Analysis, Addison Wesley, 1974.

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

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: