Mathematics 1

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Sets and mappings. Sequences of real numbers and their limits. Real functions; introduction to elementary functions. Limits of functions, continuity. Derivative. Total differential, Taylor polynomial. Local extrema and graphing. Applications of differentiation. Indefinite integral, basic integration methods. Integrating some special types of functions. Definite integral. Applications of integration.

Requirements:

Syllabus of lectures:

1. Real and complex numbers

2. Limit of a sequence

3. Function, limit, continuity

4. Derivative

5. Elementary functions

6. Applications of the derivative, Taylor formula

7. Local extrema. Graphing functions

8. Antiderivatives

9. Integration of rational and irrational functions

10. Integration of trigonometric and other functions

11. Riemann integral

12. Improper integrals

13. Applications of integrals

Syllabus of tutorials:

1. Real and complex numbers

2. Limit of a sequence

3. Function, limit, continuity

4. Derivative

5. Elementary functions

6. Applications of the derivative, Taylor formula

7. Local extrema. Graphing functions

8. Antiderivatives

9. Integration of rational and irrational functions

10. Integration of trigonometric and other functions

11. Riemann integral

12. Improper integrals

13. Applications of integrals

Study Objective:

Study materials:

[1] M. Demlová, J. Hamhalter: Calculus I. ČVUT, Praha, 1994.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: