Mathematics 1

Lecturer:

Paola Vivi

Tutor:

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:

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	roomZ4:B2-326 Vivi P. 13:30–17:00 ODD WEEK (lecture parallel1 parallel nr.101) Zikova ulice Konzultační místnost
Tue
Fri
Thu	roomZ4:B2-326 Vivi P. 13:30–15:15 (lecture parallel1) Zikova ulice Konzultační místnostroomZ4:B2-326 Vivi P. 15:15–17:00 (lecture parallel1) Zikova ulice Konzultační místnost
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Cybernetics and Robotics - Robotics (compulsory course in the program)
• Cybernetics and Robotics - Senzors and Instrumention (compulsory course in the program)
• Cybernetics and Robotics - Systems and Control (compulsory course in the program)
• Cybernetics and Robotics (compulsory course in the program)