Course detail

# Mathematics 5 (R)

FAST-CA006Acad. year: 2022/2023

Errors in numeric calculations, solvig transcendental equations in one and several unknowns using iteration methods. Iteration methods used to solve systems of linear algebraic equations. Interpolating and approximating functions. Numerical differentiation and integration and their application to solving boundary value problems for the ordinary differential equations. Applications given by the specialization.

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Course curriculum

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

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Basic literature

VALA J.: Numerická matematika. FAST VUT v Brně 2021.

(CS)Recommended reading

Classification of course in study plans

- Programme N-P-E-SI (N) Master's
branch R , 1. year of study, winter semester, compulsory

- Programme N-K-C-SI (N) Master's
branch R , 1. year of study, winter semester, compulsory

- Programme N-P-C-SI (N) Master's
branch R , 1. year of study, winter semester, compulsory

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