Differential Equations&Numerical Methods
Code  Completion  Credits  Range  Language 

BE5B01DEN  Z,ZK  7  4P+2C  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

This course introduces students to the classical theory of ordinary differential equations (separable and linear ODEs) and also to bsics of numerical methods (errors in calculations and stability, numerical solutions of algebraic and differential equations and their systems). The course takes advantage of the synnergy between theoretical and practical point of view.
 Requirements:

Calculus 1
Linear Algebra
 Syllabus of lectures:

1. Solving ODEs by separation. Slope field, stability of equilibria.
2. Errors in computing.
3. Approximating derivative, order of method.
4. Numerical integration.
5. Numerical solution of differential equations (Euler method, RungeKutta).
6. Linear ODEs  homogeneous and nonhomogeneous (method of undetermined coefficients, variation method).
7. Numerical solution of higher order ODEs.
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). Complexity of algorithm. Stability.
10. Iteration methods for solving systems of linear equations (GaussSeidel).
11. Systems of ODEs. Stability of solutions.
12. Numerical methods for determining eigenvalues and eigenvectors of matrices.
13. Applications of differential equations.
 Syllabus of tutorials:

1. Ordinary differential equations solvable by separation.
2. Analysis of solutions (stability, existence).
3. Getting to know the system, error in calculations.
4. Numerical integration.
5. Numerical solution of differential equations.
6. Homogeneous linear differential equations.
7. Equations with quasipolynomial right handside. Method of undetermined coefficients.
8. Numerical methods for finding roots of functions.
9. Homogeneous systems of linear ODEs.
10. Systems of linear ODEs.
11. Systems of linear ODEs numerically.
12. Eigenvalues and eigenvectors of matrices numerically.
13. Review of differential equations.
 Study Objective:

The aim is to acquire basic skills in reallife approaches to solving basic mathematical problems, and to get acquainted with theoretical foundations of ODE and numerical methods.
 Study materials:

[1] Habala P.: Ordinary Differential Equations And Numerical Analysis, online, 2020, popřípadě kratší verze v češtině.
[2] Epperson, J.F.: An Introduction to Numerical Methods and Analysis. John Wiley & Sons, 2013.
[3] William E. Boyce, Richard C. DiPrima, Douglas B. Meade: Boyce's Elementary Differential Equations and Boundary Value Problems, 11. vydání, 2017.
 Note:
 Further information:
 https://math.fel.cvut.cz/en/people/habala/teaching/dene.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Electrical Engineering and Computer Science (EECS) (compulsory course in the program)
 Electrical Engineering and Computer Science (EECS) (compulsory course in the program)