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Elements of Higher Mathematics

Type of study Follow-up Master
Language of instruction English
Code 470-4123/02
Abbreviation EVM
Course title Elements of Higher Mathematics
Credits 6
Coordinating department Department of Applied Mathematics
Course coordinator Mgr. Bohumil Krajc, Ph.D.

Subject syllabus

1.Diferential of a function of several variables. Gradient method.
2.Diferential of a composite function. Transformation of variables in the differential expressions.
3.Approximation of function . Taylor's theorem . Conditions for the existence of local extremes.
4.Numerical derivative. Approximate solutions of equations.
5.Theorem about implicitly defined function. Constrained extremes.
6.Construction of integral sums, numerical integration .
7.Definition of multiple integrals. Selected applications.
8.Fubini`s theorems. Substitution in multiple integrals . Geometric interpretation of Jacobian .
9.Theorems about the existence and uniqueness of solutions of initial value problems for ordinary differential equations. Euler's method.
10.Transformation of variables in differential equations .
11.Potential and its use for solving exact equations.
12.Ordinary differential equations of higher orders. Solving linear differential equations. Boundary value problems .

Literature

• W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1964
• W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

Advised literature

• M. Braun: Differential Equations and Their Applications. Springer, Berlin 1978.