Subject description - A8B01DEN

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A8B01DEN Differential Equations&Numerical Methods
Roles:P Extent of teaching:4P+2C
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:7
Tutors:  Semester:L

Web page:

http://math.feld.cvut.cz/habala/teaching/den.htm

Anotation:

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

Study targets:

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

Course outlines:

1. Numerical integration.
2. Numerical methods for finding roots of functions (bisection method, Newton method, iteration method).
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. Systems of linear differential equations with constant coefficients (elimination method, method of eigenvalues).
9. Finite methods of solving systems of linear equations (GEM, LU decomposition).
10. Iteration methods for solving systems of linear equations.
11. Numerical methods for determining eigenvalues and eigenvectors of matrices.
12. Partial differential equations (basic types, applications in physics).
13. Gamma function. Bessel?s differential equations. Bessel functions of the first kind (series). Application: solving the wave equation.
14. Back-up class.

Exercises outline:

1. Getting to know the system, error in calculations.
2. Numerical methods for finding roots of functions.
3. Ordinary differential equations solvable by separation.
4. Numerical solution of differential equations.
5. Homogeneous linear differential equations.
6. Basis of solutions of homogeneous linear differential equations. Equations with quasipolynomial right hand-side.
7. Method of undetermined coefficients.
8. Systems of linear differential equations.
9. Systems of linear equations, interpretation of results (LU).
10. Iteration methods for solving systems of linear equations.
11. Eigenvalues and eigenvectors of matrices.
12. Partial differential equations.
13. Bessel functions and PDE.
14. Back-up class.

Literature:

1. Epperson, J.F.: An Introduction to Numerical Methods and Analysis. John Wiley & Sons, 2007.
2. Lecture notes for the course.

Requirements:

Mathematics - Calculus 1 Linear Algebra

Keywords:

differential equations, numerical methods, numerical analysis

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOES Common courses P 2

Page updated 18.4.2024 14:51:52, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: prof. Ing. Jiří Jakovenko, Ph.D.