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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Differential Equations&Numerical Methods

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Code Completion Credits Range Language
BE5B01DEN Z,ZK 7 4P+2C
Enrollement in the course requires an successful completion of the following courses:
Calculus 1 (BE5B01MA1)
Lecturer:
Petr Habala (guarantor)
Tutor:
Petr Habala (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

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.

Requirements:

Mathematics - Calculus 1

Linear Algebra

Syllabus of lectures:

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.

Syllabus of tutorials:

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.

Study Objective:

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.

Study materials:

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

2. Lecture notes for the course.

Note:
Further information:
http://math.feld.cvut.cz/habala/teaching/den-e.htm
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomT2:A4-204
Habala P.
14:30–16:00
(lecture parallel1)
Dejvice
Učebna
Fri
roomT2:C4-459
Habala P.
09:15–10:45
(lecture parallel1)
Dejvice
Laborator počítače
roomT2:C4-459
Habala P.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
Laborator počítače
Thu
roomT2:C4-459

16:15–17:45
(lecture parallel1
parallel nr.102)

Dejvice
Laborator počítače
Fri
The course is a part of the following study plans:
Data valid to 2020-01-20
For updated information see http://bilakniha.cvut.cz/en/predmet4355806.html