CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics-Calculus1

Code Completion Credits Range Language
A8B01MC1 Z,ZK 7 4P+2S Czech
Lecturer:
Josef Tkadlec (guarantor)
Tutor:
Josef Tkadlec (guarantor), Josef Hekrdla
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:

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:
http://math.feld.cvut.cz/0educ/pozad/b0b01ma1.htm
Time-table for winter semester 2019/2020:
 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:D3-209Tkadlec J.14:30–16:00(lecture parallel1)DejviceT2:D3-209 roomT2:C3-51Tkadlec J.09:15–10:45(lecture parallel1parallel nr.101)DejviceT2:C3-51roomT2:D2-256Tkadlec J.16:15–17:45(lecture parallel1)DejviceT2:D2-256
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-09
For updated information see http://bilakniha.cvut.cz/en/predmet2664906.html