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Mathematics II

Credits 8
Hours per week 3 / 3 / 0
Examination C+Ex
Study Language English
Level Bachelor subject
Guarantor RNDr. Pavel Pokorný, Ph.D.

Summary

Mathematics II develops skills obtained in Mathematics I to a level required in Master Program.

Syllabus

1. Linear space, base, dimension. The space C(I). Linear mapping.
2. Linear differential equations of n-th order.
3. The system two linear and nonlinear differential equations of the first order.
4. Predator-Prey models: Lotka-Wolterra System.
5. Geometry in R^3 (R^n). Metrics in R^n.
6. Differential calculus in R^n. The functions of two and more variables.
7. Directional and partial derivatives. Tangent plane. Gradient. Newton’s method.
8. Taylor’s formula. The Hessian and extreme values. Method of least squares.
9. Implicit function theory.
10. Line integral of scalar and vector field.
11. Differential form, exact differential form, Potential vector field.
12. Line integrals independent of the path.
13. Double integrals. Fubini theorem. Substitution in double integral. Improper integrals.
14. Triple integrals. Applications. Cylindrical and spherical coordinates.

Literature

A: K. Rektorys: Survey of Applicable Mathemaics, Springer 2nd edition (March 31, 1994)

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