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« one step back EDUCATION

Mathematics II (N413003SIS)

Lecture Exercise Laboratory Examination Credits
3 3 0 Z+Zk 8
   

Annotation:

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.

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.