prof. Ing. Jiří Vala, CSc.

Institute of Mathematics and Descriptive Geometry (MAT)

The students should understand the basic principles of numeric calculation, the factors that influence numeric calculation. They should be able to solve selected basic problems in numerical mathematics, understand the principle of iteration methods for solving the equation f(x)=0 and systems of linear algebraic equations mastering the calculation algorithms. They should learn how to get the basics of interpolation and approximation of functions to solve practical problems. They should be acquainted with the principles of numerical differentiation to be able to numerically solve boundary problems for ordinary differential equations. They should be able to numerically solve definite integrals.

Basic notions of the theory of functions of one real variable (derivative, limit, continuos functions, elementary functions). Calculating integrals of functions of one variable, knowing about their basic applications.

Not applicable.

Not applicable.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

Successful completion of the scheduled tests and submission of solutions to problems assigned by the teacher for home work. Unless properly excused, students must attend all the workshops. The result of the semester examination is given by the sum of maximum of 70 points obtained for a written test and a maximum of 30 points from the seminar.

Czech

Not applicable.

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

The students should understand the basic principles of numeric calculation, the factors that influence numeric calculation. They should be able to solve selected basic problems in numerical mathematics, understand the principle of iteration methods for solving the equation f(x)=0 and systems of linear algebraic equations mastering the calculation algorithms. They should learn how to get the basics of interpolation and approximation of functions to solve practical problems. They should be acquainted with the principles of numerical differentiation to be able to numerically solve boundary problems for ordinary differential equations. They should be able to numerically solve definite integrals.

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

• Programme N-P-C-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  branch S , 1. year of study, winter semester, 4 credits, compulsory
  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

• Programme N-K-C-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

• Programme N-P-E-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

• Programme N-K-C-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

• Programme N-P-E-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

• Programme N-K-C-SI (N) Master's

  branch S , 1. year of study, winter semester, 4 credits, compulsory
  

13 hours, compulsory

prof. Ing. Jiří Vala, CSc.

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