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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

Differencial Equations and Numerical Analysis

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Code Completion Credits Range Language
B0B01DRN Z,ZK 4 2P+2C Czech
The course cannot be taken simultaneously with:
Differential Equations&Numerical Methods (A8B01DEN)
Lecturer:
Petr Habala (guarantor)
Tutor:
Petr Habala (guarantor), Josef Dvořák, Daniel Gromada, Karel Pospíšil
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, Runge-Kutta).

6. Linear ODEs - homogeneous and non-homogeneous (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 (Gauss-Seidel).

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 hand-side. 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 real-life 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.

Alternativy:

[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/cz/lide/habala/teaching/drn.html
Time-table for winter semester 2021/2022:
Time-table is not available yet
Time-table for summer semester 2021/2022:
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
roomT4:D2-256
Habala P.
12:45–14:15
(lecture parallel1)
Dejvice
Posluchárna 256
Tue
Wed
roomT2:C4-459
Habala P.
11:00–12:30
(lecture parallel1
parallel nr.119)

Dejvice
Laborator počítače
roomT2:C4-459
Gromada D.
14:30–16:00
ODD WEEK

(lecture parallel1
parallel nr.105)

Dejvice
Laborator počítače
roomT2:C4-459
Gromada D.
16:15–17:45
ODD WEEK

(lecture parallel1
parallel nr.106)

Dejvice
Laborator počítače
roomT2:C4-459

18:00–19:30
ODD WEEK

(lecture parallel1
parallel nr.112)

Dejvice
Laborator počítače
roomT2:C4-459
Gromada D.
12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.107)

Dejvice
Laborator počítače
roomT2:A4-202a
Gromada D.
14:30–16:00
EVEN WEEK

(lecture parallel1
parallel nr.105)

Dejvice
Ucebna
roomT2:A4-202a
Gromada D.
16:15–17:45
EVEN WEEK

(lecture parallel1
parallel nr.106)

Dejvice
Ucebna
roomT2:A4-202a

18:00–19:30
EVEN WEEK

(lecture parallel1
parallel nr.112)

Dejvice
Ucebna
roomT2:A4-202a
Gromada D.
12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.107)

Dejvice
Ucebna
roomT2:C4-459
Pospíšil K.
14:30–16:00
EVEN WEEK

(lecture parallel1
parallel nr.116)

Dejvice
Laborator počítače
roomT2:A4-202a
Pospíšil K.
16:15–17:45
ODD WEEK

(lecture parallel1
parallel nr.117)

Dejvice
Ucebna
roomT2:A4-202a

18:00–19:30
ODD WEEK

(lecture parallel1
parallel nr.118)

Dejvice
Ucebna
roomT2:A4-202a
Pospíšil K.
12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.115)

Dejvice
Ucebna
roomT2:A4-202a
Pospíšil K.
14:30–16:00
ODD WEEK

(lecture parallel1
parallel nr.116)

Dejvice
Ucebna
roomT2:C4-459
Pospíšil K.
16:15–17:45
EVEN WEEK

(lecture parallel1
parallel nr.117)

Dejvice
Laborator počítače
roomT2:C4-459

18:00–19:30
EVEN WEEK

(lecture parallel1
parallel nr.118)

Dejvice
Laborator počítače
roomT2:C4-459
Pospíšil K.
12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.115)

Dejvice
Laborator počítače
Thu
roomT2:C4-459

09:15–10:45
EVEN WEEK

(lecture parallel1
parallel nr.108)

Dejvice
Laborator počítače
roomT2:A4-202b
Habala P.
12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.101)

Dejvice
Učebna
roomT2:A4-202b
Pospíšil K.
14:30–16:00
ODD WEEK

(lecture parallel1
parallel nr.110)

Dejvice
Učebna
roomT2:A4-203a
Habala P.
16:15–17:45
EVEN WEEK

(lecture parallel1
parallel nr.120)

Dejvice
Učebna
roomT2:A4-202b

09:15–10:45
ODD WEEK

(lecture parallel1
parallel nr.108)

Dejvice
Učebna
roomT2:C4-459
Habala P.
12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.101)

Dejvice
Laborator počítače
roomT2:C4-459
Pospíšil K.
14:30–16:00
EVEN WEEK

(lecture parallel1
parallel nr.110)

Dejvice
Laborator počítače
roomT2:C4-459
Habala P.
16:15–17:45
ODD WEEK

(lecture parallel1
parallel nr.120)

Dejvice
Laborator počítače
roomT2:C4-459

11:00–12:30
EVEN WEEK

(lecture parallel1
parallel nr.109)

Dejvice
Laborator počítače
roomT2:A4-202b

14:30–16:00
EVEN WEEK

(lecture parallel1
parallel nr.111)

Dejvice
Učebna
roomT2:A4-203a
Pospíšil K.
16:15–17:45
ODD WEEK

(lecture parallel1
parallel nr.122)

Dejvice
Učebna
roomT2:A4-202b

11:00–12:30
ODD WEEK

(lecture parallel1
parallel nr.109)

Dejvice
Učebna
roomT2:C4-459

14:30–16:00
ODD WEEK

(lecture parallel1
parallel nr.111)

Dejvice
Laborator počítače
roomT2:C4-459
Pospíšil K.
16:15–17:45
EVEN WEEK

(lecture parallel1
parallel nr.122)

Dejvice
Laborator počítače
roomT2:A4-202b

12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.124)

Dejvice
Učebna
roomT2:C4-459
Habala P.
16:15–17:45
ODD WEEK

(lecture parallel1
parallel nr.123)

Dejvice
Laborator počítače
roomT2:C4-459

12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.124)

Dejvice
Laborator počítače
roomT2:A4-203a
Habala P.
16:15–17:45
EVEN WEEK

(lecture parallel1
parallel nr.123)

Dejvice
Učebna
Fri
roomT2:A4-202b
Dvořák J.
09:15–10:45
ODD WEEK

(lecture parallel1
parallel nr.102)

Dejvice
Učebna
roomT2:A4-202b
Dvořák J.
11:00–12:30
ODD WEEK

(lecture parallel1
parallel nr.103)

Dejvice
Učebna
roomT2:C4-459
Dvořák J.
12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.104)

Dejvice
Laborator počítače
roomT2:C4-459
Dvořák J.
09:15–10:45
EVEN WEEK

(lecture parallel1
parallel nr.102)

Dejvice
Laborator počítače
roomT2:C4-459
Dvořák J.
11:00–12:30
EVEN WEEK

(lecture parallel1
parallel nr.103)

Dejvice
Laborator počítače
roomT2:A4-202b
Dvořák J.
12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.104)

Dejvice
Učebna
roomT2:C4-459
Gromada D.
09:15–10:45
ODD WEEK

(lecture parallel1
parallel nr.121)

Dejvice
Laborator počítače
roomT2:C4-459
Gromada D.
11:00–12:30
ODD WEEK

(lecture parallel1
parallel nr.113)

Dejvice
Laborator počítače
roomT2:C4-459
Gromada D.
12:45–14:15
ODD WEEK

(lecture parallel1
parallel nr.114)

Dejvice
Laborator počítače
roomT2:A4-202b
Gromada D.
09:15–10:45
EVEN WEEK

(lecture parallel1
parallel nr.121)

Dejvice
Učebna
roomT2:A4-202b
Gromada D.
11:00–12:30
EVEN WEEK

(lecture parallel1
parallel nr.113)

Dejvice
Učebna
roomT2:A4-202b
Gromada D.
12:45–14:15
EVEN WEEK

(lecture parallel1
parallel nr.114)

Dejvice
Učebna
The course is a part of the following study plans:
Data valid to 2022-08-13
For updated information see http://bilakniha.cvut.cz/en/predmet4681106.html