Name of subject: Mathematics II
Department: Department of mathematics
Lecturer

RNDr. Pavel Pokorný, PhD.

Range: 3/3 assesment, exam 
Credit:   8 

 Sylabus:

  1. Euclidean space Rn, metric, norm, properties of subsets of Rn.
  2. Differential calculus in R^n. The functions of two and more variables. Directional and partial derivatives. Tangent plane. Gradient.
  3. Taylor’s formula. Newton’s method. The Hessian and extreme values. Method of least squares.
  4. Implicit function theory.
  5. Plane and space curves defined parametrically, the tangent vector to the curve and its physical meaning. Length of the curve.
  6. Line integral of vector field.
  7. Differential form, exact differential form, Potential vector field. Line integrals independent of the path.
  8. Double and triple integrals. Fubini theorem.
  9. Substitution in double integral. Improper integrals. Applications. Cylindrical and spherical coordinates.
  10. Linear space, base, dimension. The space C(I).
  11. Linear mapping. Inverse matrix. Matrix equations.
  12. Differential equations. The method of separation of variables
  13. Linear differential equations, method of variation of constants.
  14. The system two linear and nonlinear differential equations of the first order. Predator-Prey models: Lotka-Wolterra System.