Mathematics Analyze

The course cannot be taken simultaneously with:

Mathematics 1 (Y01MA1)

Lecturer:

Petr Habala (gar.)

Tutor:

Petr Habala (gar.), Vojtěch Bartík, Miluše Hyánková, Eva Nováková, Ladislav Průcha, Vlasta Sedláčková

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:

Time-table for winter semester 2011/2012:

	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	roomZ4:B3-220 Hyánková M. 09:15–10:45 (lecture parallel1 parallel nr.112) Zikova ulice CvicebnaroomZ4:B3-220 Hyánková M. 11:00–12:30 (lecture parallel1 parallel nr.106) Zikova ulice CvicebnaroomZ4:B3-215 Nováková E. 12:45–14:15 (lecture parallel1 parallel nr.102) Zikova ulice CvicebnaroomZ4:B3-215 Nováková E. 14:30–16:00 (lecture parallel1 parallel nr.103) Zikova ulice CvicebnaroomZ4:B3-215 Hyánková M. 16:15–17:45 (lecture parallel1 parallel nr.101) Zikova ulice Cvicebna roomZ4:B3-215 Nováková E. 11:00–12:30 (lecture parallel1 parallel nr.107) Zikova ulice CvicebnaroomZ4:B3-220 Habala P. 12:45–14:15 (lecture parallel1 parallel nr.114) Zikova ulice CvicebnaroomZ4:B3-220 Hyánková M. 14:30–16:00 (lecture parallel1 parallel nr.113) Zikova ulice Cvicebna
Fri	roomT2:A4-205 11:00–12:30 (lecture parallel1 parallel nr.118) Dejvice UčebnaroomT2:A4-202a Hyánková M. 12:45–14:15 (lecture parallel1 parallel nr.115) Dejvice UcebnaroomT2:D2-256 Habala P. 16:15–17:45 (lecture parallel1) Dejvice Posluchárna
Thu	roomZ4:B3-220 Nováková E. 07:30–09:00 (lecture parallel1 parallel nr.105) Zikova ulice CvicebnaroomZ4:B3-220 Nováková E. 09:15–10:45 (lecture parallel1 parallel nr.104) Zikova ulice CvicebnaroomT2:D2-256 Habala P. 12:45–14:15 (lecture parallel1) Dejvice Posluchárna
Fri	roomZ4:B3-215 Nováková E. 07:30–09:00 (lecture parallel1 parallel nr.111) Zikova ulice CvicebnaroomZ4:B3-214 Hyánková M. 09:15–10:45 (lecture parallel1 parallel nr.109) Zikova ulice CvicebnaroomZ4:B3-214 Hyánková M. 11:00–12:30 (lecture parallel1 parallel nr.108) Zikova ulice CvicebnaroomZ4:B3-214 14:30–16:00 (lecture parallel1 parallel nr.117) Zikova ulice CvicebnaroomZ4:B3-214 16:15–17:45 (lecture parallel1 parallel nr.116) Zikova ulice Cvicebna roomZ4:B3-215 Nováková E. 09:15–10:45 (lecture parallel1 parallel nr.110) Zikova ulice Cvicebna

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

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