Mathematics 1

Lecturer:

Josef Tkadlec (gar.)

Tutor:

Josef Tkadlec (gar.), Lidmila Gabrielová, Josef Hekrdla, Vlasta Sedláčková, Jana Šnupárková

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-Leibnitz 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.

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-Leibnitz 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.

Study Objective:

Study materials:

1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994

2.P. Pták: Calculus II. ČVUT Praha, 1997.

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:B3-218 14:30–16:00 (lecture parallel1 parallel nr.110) Zikova ulice PoslucharnaroomT2:C4-364 Sedláčková V. Šnupárková J. 16:15–17:45 (lecture parallel1 parallel nr.105) Dejvice CvicebnaroomT2:C4-364 Sedláčková V. Šnupárková J. 18:00–19:30 (lecture parallel1 parallel nr.106) Dejvice Cvicebna roomZ4:B3-218 16:15–17:45 (lecture parallel1 parallel nr.109) Zikova ulice Poslucharna
Fri	roomZ4:B3-218 Tkadlec J. 07:30–09:00 (lecture parallel1 parallel nr.103) Zikova ulice PoslucharnaroomZ4:B3-218 Tkadlec J. 09:15–10:45 (lecture parallel1 parallel nr.101) Zikova ulice PoslucharnaroomT2:D3-209 Tkadlec J. 16:15–17:45 (lecture parallel1) Dejvice Posluchárna roomT2:A4-205 Sedláčková V. Gabrielová L. 07:30–09:00 (lecture parallel1 parallel nr.104) Dejvice UčebnaroomT2:A4-205 Sedláčková V. Gabrielová L. 09:15–10:45 (lecture parallel1 parallel nr.102) Dejvice Učebna
Thu	roomKN:E-107 Tkadlec J. 14:30–16:00 (lecture parallel1) Karlovo nám. Zengerova posluchárna K1
Fri	roomT2:C4-154 Sedláčková V. Hekrdla J. 09:15–10:45 (lecture parallel1 parallel nr.108) Dejvice CvičebnaroomT2:C4-154 Sedláčková V. Hekrdla J. 11:00–12:30 (lecture parallel1 parallel nr.107) Dejvice Cvičebna

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Kybernetika a robotika - Robotika (compulsory course in the program)
• Kybernetika a robotika - Senzory a přístrojová technika (compulsory course in the program)
• Kybernetika a robotika - Systémy a řízení (compulsory course in the program)
• Kybernetika a robotika - před rozřazením do oborů (compulsory course in the program)