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Mathematics II
| Type of study | Bachelor |
|---|---|
| Language of instruction | Czech |
| Code | 230-0302/01 |
| Abbreviation | MII |
| Course title | Mathematics II |
| Credits | 5 |
| Coordinating department | Department of Mathematics |
| Course coordinator | Mgr. Jakub Stryja, Ph.D. |
Subject syllabus
1. Integrational calculus of function of one veriable. Primitive function and undefinite integral. Integration of elementary functions.
2. Basic integrational methods - per partes and substitution.
3. Integration of rational functions.
4. Integration of goniometric functions and irational functions.
5. Definite integral: basic terms, their properties, Newton-Leibniz theorem. Geometrical meaning of definite integral. Substitution and per partes in definite integral.
6. Geometrical applications of definite integral - length of a curve, volume and surface of a rotating body.
7. Differential calculus of functions of two variables: its definition, graph, limits and continuity, partial derivatives of the first and higher order.
8. Equation of a tangential plane and normal to a surface. Local extrema of functions of two variables.
9. Constrained extrema of functions of two variables. Function given implicitly and its derivative.
10. Ordinary differential equations of first order: General, particular and singular solutions. Separable equations.
11. Homogeneous differential equations.
12. 1st order linear differential equation - method of variation of arbitrary constants
13. 2nd order linear differential equation with constant coefficients - method of undetermined coefficients.
14. Reserve
2. Basic integrational methods - per partes and substitution.
3. Integration of rational functions.
4. Integration of goniometric functions and irational functions.
5. Definite integral: basic terms, their properties, Newton-Leibniz theorem. Geometrical meaning of definite integral. Substitution and per partes in definite integral.
6. Geometrical applications of definite integral - length of a curve, volume and surface of a rotating body.
7. Differential calculus of functions of two variables: its definition, graph, limits and continuity, partial derivatives of the first and higher order.
8. Equation of a tangential plane and normal to a surface. Local extrema of functions of two variables.
9. Constrained extrema of functions of two variables. Function given implicitly and its derivative.
10. Ordinary differential equations of first order: General, particular and singular solutions. Separable equations.
11. Homogeneous differential equations.
12. 1st order linear differential equation - method of variation of arbitrary constants
13. 2nd order linear differential equation with constant coefficients - method of undetermined coefficients.
14. Reserve
E-learning
Literature
Advised literature
[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis.
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2