 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Mathematics-Calculus1

Code Completion Credits Range Language
A8B01MC1 Z,ZK 7 4P+2S Czech
Garant předmětu:
Lecturer:
Martin Křepela
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Requirements:

See web page.

Syllabus of lectures:

1. Elementary functions. Limit and continuity of functions.

2. Derivative of functions, its properties and applications.

3. Mean value theorem. L'Hospital's rule.

4. Limit of sequences. Taylor polynomial.

5. Local and global extrema and graphing functions.

6. Indefinite integral, basic integration methods.

7. Integration of rational and other types of functions.

8. Definite integral (using sums). Newton-Leibniz formula.

9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.

10. Improper integral.

11. Differential equations - formulation of the problem. Separation of variables.

12. First order linear differential equations (variation of parameter).

13. Applications. Numerical aspects.

14. Reserve.

Syllabus of tutorials:

1. Elementary functions. Limit and continuity of functions.

2. Derivative of functions, its properties and applications.

3. Mean value theorem. L'Hospital's rule.

4. Limit of sequences. Taylor polynomial.

5. Local and global extrema and graphing functions.

6. Indefinite integral, basic integration methods.

7. Integration of rational and other types of functions.

8. Definite integral (using sums). Newton-Leibniz formula.

9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.

10. Improper integral.

11. Differential equations - formulation of the problem. Separation of variables.

12. First order linear differential equations (variation of parameter).

13. Applications. Numerical aspects.

14. Reserve.

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:
https://moodle.fel.cvut.cz/courses/A8B01MC1
Time-table for winter semester 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT2:C4-363Tkadlec J.11:00–12:30(lecture parallel1parallel nr.101)DejviceCvicebna roomT2:D3-209Křepela M.14:30–16:00(lecture parallel1)DejviceT2:D3-209 roomT2:C3-5109:15–10:45(lecture parallel1parallel nr.102)DejviceT2:C3-51roomT4:D2-256Křepela M.16:15–17:45(lecture parallel1)DejvicePosluchárna 256
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-12-08
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet2664906.html