Mathematical Analysis B 3

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

Differential equations - basic types of differential equations of the first order, differential equations of the second order - particular cases. Linear differential equations. Convergence of integral. Power set, convergence, continuity, differentiation and integration of power set. Expansion of function to power set, Taylor's theorem. Quadratic forms and quadrics.

Requirements:

818MA1 - Mathematical analysis 1

818MA2 - Mathematical analysis 2

Syllabus of lectures:

1.Differential equations of the first order with separable variables

2.Linear differential equations of the first order

3.Particular cases of differential equations of the second order

4.Linear differential equations of the second order with constant coefficients

5.Convergence of integral

6.Laws of the mean of integral calculus, absolute convergence

7.Power set and its radius of convergence

8.Radius of convergence of power set

9.Differentiation, integration and continuity of power set

10.Expansion of function to power set, Taylor's theorem

11.Expansion of function to power set

12.Quadratic functions, quadrics

13.Quadratic forms

Syllabus of tutorials:

1.Differential equations of the first order with separable variables

2.Linear differential equations of the first order

3.Particular cases of differential equations of the second order

4.Linear differential equations of the second order with constant coefficients

5.Convergence of integral

6.Laws of the mean of integral calculus, absolute convergence

7.Power set and its radius of convergence

8.Radius of convergence of power set

9.Differentiation, integration and continuity of power set

10.Expansion of function to power set, Taylor's theorem

11.Expansion of function to power set

12.Quadratic functions, quadrics

13.Quadratic forms

Study Objective:

Knowledge:

Basic types of differential equations, convergence of integral, power sets, types of quadratic forms and quadrics.

Abilities:

Solve of differential equation, decision about convergence of integral, function expansion to power set, define type of quadratic form, drawing of quadric.

Study materials:

Compulsory literature:

[1] E. Dontová: Matematika I, Vydavatelství ČVUT, Praha 1993

[2] E. Dontová: Matematika II, Vydavatelství ČVUT, Praha 1994

[3] E. Dontová: Matematika III, Vydavatelství ČVUT, Praha 1995

Recommended literature:

[4] M. Krbálek: Matematická analýza III, Vydavatelství ČVUT, Praha 2008

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Applications of Informatics in Natural Sciences (compulsory course in the program)