Mathematical Analysis B 3

Course guarantor:

Milan Krbálek

Lecturer:

Kateřina Horaisová

Tutor:

Kateřina Horaisová

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. Quadratic forms and quadrics. Sequences of functions. Series of functions. Power series, Taylor series.

Requirements:

801MAN1 - Mathematical analysis 1

801MAN2 - 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.Quadratic functions, quadrics

6.Quadratic forms

7. Sequences of functions.

8. Series of functions.

9.Power set and its radius of convergence

10.Differentiation, integration and continuity of power set

11. Taylor series.

12.Expansion of function to Taylor series

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.Quadratic functions, quadrics

6.Quadratic forms

7. Sequences of functions.

8. Series of functions.

9.Power set and its radius of convergence

10.Differentiation, integration and continuity of power set

11. Taylor series.

12.Expansion of function to Taylor series

Study Objective:

Knowledge:

Basic types of differential equations, types of quadratic forms and quadrics, sequences and series of functions, power series, Taylor series.

Abilities:

Solving a differential equation, determining the type of quadratic form, investigation of quadrics, investigation of uniform convergence of sequences and series of functions, development of a function into a power series.

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

[4] M. Krbálek: Matematická analýza III, Vydavatelství ČVUT, Praha 2019

Note:

Time-table for winter semester 2024/2025:

	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	roomDC:P4 Horaisová K. 08:00–11:50 (lecture parallel1) Decin
Tue
Wed	roomDC:P4 Horaisová K. Eichler P. 08:00–11:50 (parallel nr.101) Decin
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

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