Mathematics 1

Lecturer:

Josef Tkadlec (gar.)

Tutor:

Josef Tkadlec (gar.), Lidmila Gabrielová, Eva Nováková, Vlasta Sedláčková, Petr Švec

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: