Mathematics 1

The course cannot be taken simultaneously with:

Mathematics Analyze (A7B01MAA)

The course is a substitute for:

Mathematics Analyze (A7B01MAA)

Lecturer:

Petr Habala (gar.)

Tutor:

Petr Habala (gar.), Eva Nováková

Supervisor:

Department of Mathematics

Synopsis:

This course is an introduction to differential and integral calculus. It covers basic properties of functions, limits of functions, derivative and its applications (graphing, Taylor polynomial) and definite/indefinite integral with its applications, sequences and series. At the end we also introduce calculus of more variables.

Requirements:

See http://math.feld.cvut.cz/0educ/pozad/y01ma1.htm

Syllabus of lectures:

1. Functions, elementary functions.

2. Limit of functions, continuity.

3. Derivative, its interpretations and applications.

4. L'Hospital's rule, Taylor polynomial.

5. Extrema of functions. Graphing functions.

6. Antiderivative, basic methods of evaluation.

7. Integrating rational functions using partial fractions.

8. Definite integral, properties and evaluation.

9. Improper integral, applications of integrals.

10. Sequences.

11. Series.

12. Introduction to functions of more variables.

13. Functions of more variables, applications of calculus.

14. Back-up class.

Syllabus of tutorials:

1. Functions.

2. Limit (elementary methods).

3. Limits, continuity.

4. Derivative.

5. Limits using l'Hospital's rule, Taylor polynomial.

6. Graphing functions, extrema.

7. Indefinite integral.

8. Indefinite integral - partial fractions.

9. Definite integral.

10. Improper integral.

11. Applications of derivative and integral.

12. Sequences, series.

13. Functions of more variables.

14. Back-up.

Study Objective:

Study materials:

1. Math Tutor http://math.feld.cvut.cz/mt

2. J. Tkadlec: Diferenciální a integrální počet funkcí jedné proměnné. ČVUT Praha 2004.

3. Web page of P. Habala

http://math.feld.cvut.cz/habala/

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Společný 1. ročník (compulsory course)
• Softwarové inženýrství (compulsory course)
• Web a multimedia (compulsory course)
• Manažerská informatika (compulsory course)
• Inteligentní systémy (compulsory course)
• Manažerská informatika (STM-A7B-přechodné) (compulsory course)
• Softwarové inženýrství (STM-A7B-přechodné) (compulsory course)
• Inteligentní systémy (STM-A7B-prechodné) (compulsory course)
• Web a multimedia (STM-A7B-přechodné) (compulsory course)