|Lecture ||Exercise ||Laboratory ||Examination
|3 ||3 ||0 ||Z+Zk
Course develops and strengthens the concepts and skills of elementary mathematics (the course of mathematics MI), particularly skills related to various disciplines of the curriculum of the magister's study.
- 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.