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

RNDr. Pavel Pokorný, PhD., Mgr. Jana Němcová, Ph.D.

Range: 3/4 assesment, exam 
Credit:   10 

 Sylabus:

  1. Elements of Mathematical Logic. Introduction to calculus.
  2. Inverse function and function composition.
  3. Continuity and limits of the functions of one variables.
  4. Derivatives.
  5. Mean value theorem, L’ Hospital’s rule.
  6. Monotone functions, extreme values of a function, asymptotes of the graph, examination of functions of one variable..
  7. Newton’s methods. Taylor’s formula with remainder. Differential.
  8. Antiderivative. Definite integral. Geometric and physical applications. Numerical integration.
  9. Techniques of integration. Improper integrals.
  10. Riemann's definition of definite integral. Selected geometric and physical applications of the integral. The mean value theorem for integrals.
  11. Linear differential equations of 1 and 2 order with constant coefficients and special right-hand sides.. Estimation method.
  12. Vectors and matrices, matrix algebra. Linear independence of vectors and rank matrix. The determinant of a matrix. Systems of linear algebraic equations. Cramer's rule.
  13. The space R^n , geometry in R^3, vectors, dot and cross products.
  14. Functions of two real variables, domain, graph, partial derivatives, gradient.