 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Calculus 1

The course is not on the list Without time-table
Code Completion Credits Range Language
AE5B01MA1 Z,ZK 7 4+2
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

It is an introductory course to calculus of functions of one variable. It starts with limit and continuity of functions, derivative and its geometrical meaning and properties, graphing of functions. Then it covers indefinite integral, basic integration methods and integrating rational functions, definite integral and its applications. It concludes with introduction to Taylor series.

Requirements:
Syllabus of lectures:

1. The real line, elementary functions and their graphs, shifting and scaling.

2. Limits and continuity, tangent, velocity, rate of change.

3. Derivative of functions, properties and applications.

4. Mean value theorem, L'Hospital's rule.

5. Higher derivatives, Taylor polynomial.

6. Local and global extrema, graphing of functions.

7. Indefinite integral, basic integration methods.

8. Integration of rational functions, more techniques of integration.

9. Definite integral, definition and properties, Fundamental Theorems of Calculus.

10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.

11. Sequences of real numbers, numerical series, tests for convergence.

12. Power series, uniform convergence, the Weierstrass test.

13. Taylor and Maclaurin series.

Syllabus of tutorials:

1. The real line, elementary functions and their graphs, shifting and scaling.

2. Limits and continuity, tangent, velocity, rate of change.

3. Derivative of functions, properties and applications.

4. Mean value theorem, L'Hospital's rule.

5. Higher derivatives, Taylor polynomial.

6. Local and global extrema, graphing of functions.

7. Indefinite integral, basic integration methods.

8. Integration of rational functions, more techniques of integration.

9. Definite integral, definition and properties, Fundamental Theorems of Calculus.

10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.

11. Sequences of real numbers, numerical series, tests for convergence.

12. Power series, uniform convergence, the Weierstrass test.

13. Taylor and Maclaurin series.

Study Objective:
Study materials:

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

2. P. Pták: Calculus II. ČVUT Praha, 1997.

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-01-19
For updated information see http://bilakniha.cvut.cz/en/predmet3415406.html