Počet kreditů | 7 |

Vyučováno v | Summer |

Rozsah výuky | 4P+2C |

Garant předmětu | |

Přednášející | |

Cvičící |

This course offers an introduction to differential equations and numerical methods. We survey major types of ordinary differential equations. For common problems (roots, systems of linear equations, ODE?s) we will show basic approaches for solving them numerically.

Mathematics - Calculus 1

Linear Algebra

The aim is to acquire basic skills in real-life approaches to solving basic mathematical problems, and to get acquainted with theoretical foundations of ODE and numerical methods.

1. Errors in computing.

2. Numerical differentiation and integration.

3. Ordinary differential equations. Existence and uniqueness of solution.

4. Numerical solution of differential equations (Euler method and others).

5. Linear differential equations with constant coefficients (structure of solution set, characteristic numbers).

6. Basis of solutions of homogeneous linear differential equations. Equations with quasipolynomial right hand-side.

7. Method of undetermined coefficients. Superposition principle. Quantitative properties of solutions.

8. Numerical methods for finding roots of functions (bisection method, Newton method, iteration method).

9. Finite methods of solving systems of linear equations (GEM, LU decomposition).

10. Iteration methods for solving systems of linear equations.

11. Systems of linear differential equations with constant coefficients (elimination method, method of eigenvalues).

12. Numerical methods for determining eigenvalues and eigenvectors of matrices.

13. Laplace transform.

1. Getting to know the system, error in calculations.

2. Ordinary differential equations solvable by separation.

3. Analysis of solutions (stability, existence).

4. Numerical solution of differential equations.

5. Homogeneous linear differential equations.

6. Equations with quasipolynomial right hand-side. Method of undetermined coefficients.

7. Variation of parameters.

8. Numerical methods for finding roots of functions.

9. Systems of linear equations, (LU, iteration).

10.Systems of linear differential equations.

11. Eigenvalues and eigenvectors of matrices.

12. Project.

13. Laplace transform.

1. Epperson, J.F.: An Introduction to Numerical Methods and Analysis. John Wiley & Sons, 2007.

2. Lecture notes for the course.