Mathematics-Calculus1

Course guarantor:

Josef Tkadlec

Lecturer:

Martin Křepela

Tutor:

Martin Křepela, Josef Tkadlec

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 2024/2025:

	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
Mon	roomT2:C4-363 Tkadlec J. 11:00–12:30 (lecture parallel1 parallel nr.101) Dejvice
Tue	roomT2:D3-209 Křepela M. 14:30–16:00 (lecture parallel1) Dejvice
Wed	roomT2:C3-51 09:15–10:45 (lecture parallel1 parallel nr.102) Dejvice roomT4:D2-256 Křepela M. 16:15–17:45 (lecture parallel1) Dejvice
Thu
Fri	roomT2:D3-309 Křepela M. 11:00–12:30 (lecture parallel1) Dejvice

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Open Electronic Systems (compulsory course in the program)
• Open Electronic Systems (compulsory course in the program)