 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Mathematical Analysis 1

Code Completion Credits Range Language
B0B01MA1 Z,ZK 7 4P+2S Czech
The course cannot be taken simultaneously with:
Mathematical Analysis 1 (B0B01MA1A)
The course is a substitute for:
Mathematical Analysis 1 (B0B01MA1A)
Lecturer:
Tutor:
Josef Tkadlec (guarantor), Josef Dvořák, Karel Pospíšil
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.Real numbers. Elementary functions.

2. Limit and continuity of functions.

3. Derivative of functions, its properties and applications.

4. Mean value theorem. L'Hospital's rule, 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. Improper integral. Application of integrals.

10. Sequences and their limits.

11. Rows, criteria of convergence.

12. Introduction to differential equations.

13. Other topics of mathematical analysis.

Syllabus of tutorials:

1.Real numbers. Elementary functions.

2. Limit and continuity of functions.

3. Derivative of functions, its properties and applications.

4. Mean value theorem. L'Hospital's rule, 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. Improper integral. Application of integrals.

10. Sequences and their limits.

11. Rows, criteria of convergence.

12. Introduction to differential equations.

13. Other topics of mathematical analysis.

Study Objective:

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

Study materials:

 J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.

Note:
Further information: