Czech

Not applicable.

After completing the course the student will be able to:
• Work with various matrix and vector norms and make their estimates.
• Solve systems of linear algebraic equations. Decide whether it is possible to solve the system using a given method.
• Find roots of nonlinear and algebraic equations with required accuracy.
• Solve systems of equations.
• Determine the dominant eigenvalue of a matrix.
• Find all eigenvalues. To the suitability of the specified procedure for finding eigenvalues.
• Find the numerical solution of initial value problems for ordinary differential equations and their systems with required accuracy.
• Find the numerical solution of partial differential equations. Work with boundary and internal points system.
• Explain the nature of the finite element method and know how to use it to solve problems on a computer.
• Select the appropriate method for a given type of task and estimate the rate of convergence of certain methods.
• Determine accuracy estimates for certain methods.

We require knowledge at the level of bachelor's degree, i.e. that students must be able to work with matrices and vectors, handle the calculation of determinants, calculate the product of a matrix and inverse matrix, know the graphs of elementary functions and methods of construction, differentiate and integrate of basic functions, solve basic types of ordinary differential equations of the first order.

Not applicable.

Teaching methods depend on types of classes. They are described in Article 7 of the Study and Examination Regulations of Brno University of Technology.

Students may be awarded
Up to 45 points for work during semester, i.e. 5 homework tasks (maximum 5 points each) and 2 practical computer homework tasks (max. 10 points each).
Up to 55 points for the written final exam. The test contains both theoretical and numerical tasks that are used to verify the orientation in the problems of numerical methods and their application. This includes tasks such as "adjust to the shape of convergence", without interpolating the end.

The subject consists of 5 tutorials and 2 practical computer classes. The distribution of topics respects topics of MMNM. The last tutorial is devoted to repetition and preparations for the exam. In computer classes examples and possible ways of programming the topics in MATLAB are included.

MMNM topics structure:
1. The principle of numerical methods, classification and propagation of errors in the numerical process, increasing the accuracy of the calculation, Banach fixed point theorem.
2. Solving systems of linear equations: an overview of finite and iterative solution methods.
3. Review of methods for solving nonlinear equations.
4. Algebraic equations and their properties, estimates of the root position, the method of determining roots of algebraic equations.
5. Solving systems of nonlinear equations. Newton and iterative methods for systems of equations.
6. Eigenvalues. Identification of the dominant eigenvalue.
7. The solution of ordinary differential equations of the first order. Basic concepts, the initial problem, one-step and multi-step methods of solution, Taylor series method.
8. Ordinary differential equations of higher order. Systems of ordinary differential equations of first order and their solutions.
9. Boundary value problems for ordinary differential equation and its solution by finite differences and finite volumes.
10. Finite element methods for ordinary differential equations.
11. Partial Differential Equations. Basic concepts, solutions of partial differential equations of the first order.
12. Classification of partial differential equations of second order. The solution of partial differential equations of second order using method of finite differences.
13. The solution of partial differential equations of second order using the finite elements method.

Not applicable.

The aim is to extend and intesify knowledge from the previous courses, namely in connexion with practical applications of the methods for solving the ordinary a partial differential equations. For this purpose two chapters summarizing the methods for solving linear and nonlinear equations precede.

Specifications of the controlled activities and ways of implementation are provided in an annual public notice of the person responsible either for the subject or for the combined form of study.

Not applicable.

Not applicable.

BAŠTINEC, J.; NOVÁK, M. Moderní numerické metody. Moderní numerické metody. Brno: 2014
BAŠTINEC, J.; NOVÁK, M. Moderní numerické metody: sbírka příkladů. Brno: FEKT, VUT v Brně, 2011.

Not applicable.