The study course is an introduction to modern mathematics. Its acquisition is necessary for the successful application of mathematical methods in dealing with technical, environmental, economical and other issues. The study course can also be considered a basis necessary to build an understanding of advanced mathematics.
The following topics are covered in the study course: analytical geometry: vectors, lines, surfaces; linear algebra: matrices, determinants, systems of linear equations; introduction to analysis: limits, continuity, differential calculus: derivative, differential and their applications; integral calculus: indefinite and definite integrals, their applications; ordinary differential equations; series; double and triple integrals.
Course contents:
- Introduction to analysis. Elementary functions. Limits. Continuity.
- Differential calculus of one variable functions. Derivatives. Applications.
- Differential calculus of two variable functions.
- Linear algebra. Matrix notation. The determinant. Operations with matrices. Simultaneous equations.
- Vectors. Operations with vectors.
- Analytical geometry. Line in a plane. Line and plane in a space.
- Complex numbers. Operations with complex numbers in Cartesian and in polar form.
- Integral calculus. Methods of integration.
- Definite integrals. Improper integrals of 1st and 2nd kind.
- Double integral and triple integral. Applications.
- Differential equations. Family of solutions. Methods of solutions.
- Series. Convergence tests. Power series. Taylor series.
- Fourier series.
