http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)
Special Topics in Mathematics
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | Czech |
| Code | 230-0403/02 |
| 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
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. Constrained extremes, Lagrange's method.
6th Global extremes. Taylor's theorem.
7th Two-dimensional integrals on a rectangle and on a general domain.
8th Calculations of two-dimensional integrals, applications in geometry and physics.
9th Three-dimensional integrals, calculation and application.
10th Line integral of the first and second kind, calculation methods.
11th Applications of curved integrals, Green's theorem, independence of the integration path.
12th Surface integrals and their calculation.
13th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.
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. Constrained extremes, Lagrange's method.
6th Global extremes. Taylor's theorem.
7th Two-dimensional integrals on a rectangle and on a general domain.
8th Calculations of two-dimensional integrals, applications in geometry and physics.
9th Three-dimensional integrals, calculation and application.
10th Line integral of the first and second kind, calculation methods.
11th Applications of curved integrals, Green's theorem, independence of the integration path.
12th Surface integrals and their calculation.
13th 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 .
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 .
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 .