CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Calculus 1

Code Completion Credits Range Language
BE5B01MA1 Z,ZK 7 4P+2S English

During a review of study plans, the course B0B01MA1A can be substituted for the course BE5B01MA1.

In order to register for the course BE5B01DEN, the student must have successfully completed the course BE5B01MA1.

Garant předmětu:
Paola Vivi
Lecturer:
Paola Vivi
Tutor:
Paola Vivi
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:

https://math.fel.cvut.cz/en/people/vivipaol/MA12015.pdf

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.

https://math.fel.cvut.cz/en/people/vivipaol/MA12015.pdf

Note:
Further information:
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA1.html
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-04-17
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4355206.html