Mathematics 1

The course is a substitute for:

Mathematics 1 (X01MA1)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Introductory course to calculus of functions of one variable. Language of mathematics, limits of sequences and functions, continuity and derivative, maximum and minimum of a function, graphing functions, Taylor polynomial. Indefinite integral, basic integration methods, integrating rational functions. Definite integral and its applications.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials. See http://math.feld.cvut.cz/0educ/pozad/xe01ma1.htm

Syllabus of lectures:

1. Sets and mappings.

2. Informal introduction to logical formulae and quantifiers as the language of mathematics.

3. Sequences of real numbers and their limits.

4. Real functions; introduction to elementary functions.

5. Limits of functions, continuity.

6. Derivative.

7. Total differential, Taylor polynomial.

8. Local extrema and graphing.

9. Applications of differentiation.

10. Indefinite integral, basic integration methods.

11. Integrating some special types of functions.

12. Definite integral.

13. Applications of integration.

14. Back-up class.

Syllabus of tutorials:

1. Sets and mappings.

2. Informal introduction to logical formulae and quantifiers as the language of mathematics.

3. Sequences of real numbers and their limits.

4. Real functions; introduction to elementary functions.

5. Limits of functions, continuity.

6. Derivative.

7. Total differential, Taylor polynomial.

8. Local extrema and graphing.

9. Applications of differentiation.

10. Indefinite integral, basic integration methods.

11. Integrating some special types of functions.

12. Definite integral.

13. Applications of integration.

14. Back-up class.

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:

• Společný plán- strukturované anglické studium (compulsory course)
• Electronics and Communication Technology - structured studies (compulsory course)
• Cybernetics and Measurements- structured studies (compulsory course)
• Heavy-current Engineering- structured studies (compulsory course)
• Computer Technology- structured studies (compulsory course)