Mathematical Analysis 1

Garant předmětu:

Josef Tkadlec

Lecturer:

Jan Hamhalter, Paola Vivi

Tutor:

Jan Hamhalter, Hana Turčinová, Paola Vivi

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 http://math.feld.cvut.cz/vivi/AD0B01MA1.htm.

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:

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

Note:

Further information:

https://moodle.fel.cvut.cz/courses/BD5B01MA1

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
Mon
Tue
Wed
Thu
Fri	roomT2:C2-83 Vivi P. 10:00–13:30 (lecture parallel1) Dejvice cvičebna

Time-table for summer 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
Mon
Tue
Wed
Thu
Fri	roomT2:C2-83 Hamhalter J. 11:00–14:15 (lecture parallel1) Dejvice cvičebna

The course is a part of the following study plans:

• Electrical Enginnering, Electronics and Communications (compulsory course in the program)