Selected parts from mathematics II.

• 39 hrs lectures

Students completing this course should be able to:
- calculate improper multiple integral on unbounded regions and from unbounded functions.
- apply a weighted function and a delta function to solving of linear differential equations.
- select an optimal solution method for given differential equation.
- investigate a stability of solutions of systems of differential equations.

The aim of this course is to introduce the basics of improper multiple integrals, systems of differential equations including of investigations of a stability of solutions of differential equations and applications of selected functions with solving of dynamical systems.

The student should be able to apply the basic knowledge of analytic geometry and mathamatical analysis on the secondary school level: to explain the notions of general, parametric equations of lines and surfaces and elementary functions.
From the BMA1 and BMA2 courses, the basic knowledge of differential and integral calculus and solution methods of linear differential equations with constant coefficients is demanded. Especially, the student should be able to calculate derivative (including partial derivatives) and integral of elementary functions.

• KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s.
• BRABEC, J., HRUZA, B.: Matematická analýza II, SNTL/ALFA, Praha 1986, 579s.
• GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2.

• ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti.

1.Some notions from differential calculus of a function of multi variables.
2.Multiple integrals.
3.Transformation of multiple integrals.
4.Improper multiple integrals.
5.Lines in Rn, undirected line integral.
6.Directed line integral, indenpedence on an
integrable way.
7.Surfaces in R3, undirected surface integral.
8.Orientation of a surface, directed surface
integral.
9.Integral theorems.
10.Systems of differential equations, elementary
methods of solving.
11.General methods of solving of differential
equations.
12. Differential transformation method for ordinary differential equations
13.Differential transformation method for delay differential equations

The student's work during the semestr (written tests and homework) is assessed by maximum 30 points.
Written examination is evaluated by maximum 70 points. It consist of seven tasks (one from improper multiple integral (10 points), three from application of a weighted function and a delta function (3 X 10 points) and three from analytical solution method of differential equations (3 x 10 points)).

Teaching methods include lectures and demonstration practises . Course is taking advantage of exercise bank and Maple exercises on server UMAT. Students have to write a single project/assignment during the course.

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.