Mathematical Analysis B 3
Code  Completion  Credits  Range  Language 

801MAN3  Z,ZK  8  4P+4C  Czech 
 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 timetable 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)