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Special Topics in Mathematics

Type of study Follow-up Master
Language of instruction English
Code 230-0403/04
Abbreviation VKM
Course title Special Topics in Mathematics
Credits 5
Coordinating department Department of Mathematics
Course coordinator doc. Ing. Martin Čermák, Ph.D.

Subject syllabus

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

E-learning

Literature

http://mdg.vsb.cz/portal/
KREML, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X.
KUČERA, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
HARSHBARGER, Ronald; REYNOLDS, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1 .

Advised literature

JAMES, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.
DOLEŽALOVÁ, Jarmila: Mathematics I, VŠB - TUO, Ostrava 2005, 80-248-0796-3.
MOORE,C: Math quations and inequalities, Science & Nature, 2014.
JAMES, G.: Modern Engineering Mathematics. Addison – Wesley Publishing
Company, Wokingham, 1994, ISBN 0-201-18504-5 .