Mathematical Analysis B 4
Code  Completion  Credits  Range  Language 

818MAB4  Z,ZK  7  2+4  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Software Engineering
 Synopsis:

Limit and continuity of function of more variables. Direction and partial derivative, first derivative and differential, derivative of composite function, derivative of highorders, Taylor's theorem. Implicit function, regular mapping, replacement of variables. Local and bound extremes of functions of more variables. Multiple integral, basic properties, Fubini's theorem, substitution theorem. Curves and curve integral of the first and the second order. Surface integral of the first and the second order. Green's theorem, Gauss's theorem, Stokes' theorem.
 Requirements:

818MA1  Mathematical analysis 1
818MA2  Mathematical analysis 2
 Syllabus of lectures:

1.Limit and continuity of function of more variables
2.Direction and partial derivative, first derivative and differential, derivative of composite function
3.Derivative of highorders, Taylor's theorem
4.Implicit function
5.Regular mapping and replacement of variables
6.Local extremes of functions
7.Bound extremes of functions
8.Multiple integral
9.Fubini's theorem, substitution theorem, Lebesgue integral
10.Curves and curve integral of the first and the second order
11.Surface integral of the first order
12.Surface integral of the second order
13.Green's theorem, Gauss's theorem, Stokes' theorem
 Syllabus of tutorials:

1.Limit and continuity of function of more variables
2.Direction and partial derivative, first derivative and differential, derivative of composite function
3.Derivative of highorders, Taylor's theorem
4.Implicit function
5.Regular mapping and replacement of variables
6.Local extremes of functions
7.Bound extremes of functions
8.Multiple integral
9.Fubini's theorem, substitution theorem, Lebesgue integral
10.Curves and curve integral of the first and the second order
11.Surface integral of the first order
12.Surface integral of the second order
13.Green's theorem, Gauss's theorem, Stokes' theorem
 Study Objective:

Knowledge:
Elements of differential and integral calculus of function of more variables.
Abilities:
Calcuation of limit, derivative, extremes, and integral of function of more variables, replacement of variables.
 Study materials:

Compulsory literature:
[1] E. Dontová: Matematika IV, Vydavatelství ČVUT, Praha 1996
Recommended literature:
[2] M. Krbálek: Matematická analýza IV, Vydavatelství ČVUT, Praha 2009
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: