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Terminated in academic year 2018/2019

Special Topics in Mathematics

Type of study Follow-up Master
Language of instruction Czech
Code 714-0513/01
Abbreviation VKM
Course title Special Topics in Mathematics
Credits 5
Coordinating department Department of Mathematics and Descriptive Geometry
Course coordinator prof. RNDr. Radek Kučera, Ph.D.

Subject syllabus

Week. Lecture
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1st Vector calculus, scalar, cross and triple product, vector functions.
2nd Differential calculus of functions of two or more real variables: domain, graph, limit and continuity.
3rd Partial derivatives, total differential, tangent plane and normal to a surface.
4th Implicit function and its derivatives.
5th Extremes of functions, calculation via derivatives.
6th Constrained extremes, Lagrange's method.
7th Global extremes. Taylor's theorem.
8th Two-dimensional integrals on a rectangle and on a general domain.
9th Calculations of two-dimensional integrals, applications in geometry and physics.
10th Three-dimensional integrals, calculation and application.
11th Line integral of the first and second kind, calculation methods.
12th Applications of curved integrals, Green's theorem, independence of the integration path.
13th Surface integrals and their calculation.
14th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.

Literature

1. Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X.
2. Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
3. Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1 .

Doporučená literatura

1. Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1 .