Czech

4

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

To understand the basic principles of numeric calculation and the factors influencing nueric calculation. Know how to solve selected basic problems of numeric mathematics. Understand iteration methods used to solve a f(x)=0 equation and systems of linear algebraic equations, practice calculation algorithms. Learn how to interpolate functions. Understand the principles of numerical differentiation to calculate numerical solutions to a boundary value problem for the ordinary differential equations. Learn how to calculate definite integrals.

Basics of the theory of functions in one variable (derivative, limit and continuity, elementary functions). Definite integrals and their basic applications.

Not applicable.

The course is taught through lectures, practical classes and self-study assignments. Attendance at lectures is optional, but attendance at classes is compulsory.

The following items are obligatory: attending exercises, solution of individual examples, successful results of all tests.

1. Errors in numerical calculations, approximation of the solutions of one equation in one real variable by bisection and by iteration
2. Approximation of the solutions of one equation in one real variable by iteration, the Newton method and its modifications
3. Norms of matrices and vectors, calculations of the inverse matrices
4. Solutions of systems of linear equations with speciál matrice and the condition numer of a matrix
5. Solutions of systems of linear equations by iteration
6. Solutions of systems of non—linear equations
7. Lagrange interpolation by polynomials and cubic splines, Hermite interpolation by polynomials and Hermite cubic splines
8. The discrete least squares Metod, numerical differentiation
9. Classical formulation of the boundary—value problem for the ODE of second order and its approximation by the finite diference method
10. Numerical integration. Variational formulation of the boundary—value problem for the ODE of second order
11. Discertization of the variational boundary—value problem for the ODE of second order by the finite element method
12. Classical and variational formulations of the boundary—value problem for the ODE of order four
13. Discertization of the variational boundary—value problem for the ODE of order four by the finite element method

Not applicable.

To understand the basic principles of numeric calculation and the factors influencing nueric calculation. Know how to solve selected basic problems of numeric mathematics. Understand iteration methods used to solve a f(x)=0 equation and systems of linear algebraic equations, practice calculation algorithms. Learn how to interpolate functions. Understand the principles of numerical differentiation to calculate numerical solutions to a boundary value problem for the ordinary differential equations. Learn how to calculate definite integrals.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Not applicable.

Not applicable.

Not applicable.

Not applicable.

13 hours, compulsory

Follows directly particular lectures.
1. Errors in numerical calculations, approximation of the solutions of one equation in one real variable by bisection and by iteration
2. Approximation of the solutions of one equation in one real variable by iteration, the Newton method and its modifications
3. Norms of matrices and vectors, calculations of the inverse matrices
4. Solutions of systems of linear equations with speciál matrice and the condition numer of a matrix
5. Solutions of systems of linear equations by iteration
6. Solutions of systems of non—linear equations
7. Lagrange interpolation by polynomials and cubic splines, Hermite interpolation by polynomials and Hermite cubic splines
8. The discrete least squares Metod, numerical differentiation
9. Classical formulation of the boundary—value problem for the ODE of second order and its approximation by the finite diference method
10. Numerical integration. Variational formulation of the boundary—value problem for the ODE of second order
11. Discertization of the variational boundary—value problem for the ODE of second order by the finite element method
12. Classical and variational formulations of the boundary—value problem for the ODE of order four
13. Discertization of the variational boundary—value problem for the ODE of order four by the finite element method