Mathematical Analysis 4

Lecturer:

Petr Kubera (gar.)

Tutor:

Petr Kubera (gar.)

Supervisor:

Synopsis:

Limit and continuity of function of more variables. Direction and partial derivative, first derivative and differential, derivative of composite function, derivative of high-orders, 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 high-orders, 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 high-orders, 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:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: