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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025
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Welcome page > Faculty of Information Technology > Department of Applied Mathematics > Differential equations

Differential equations

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Code Completion Credits Range Language
BIE-DIF Z,ZK 5 2P+2C English
Course guarantor:
Ondřej Bouchala
Lecturer:
Ondřej Bouchala, Antonella Marchesiello, Jan Valdman
Tutor:
Ondřej Bouchala, Antonella Marchesiello, Jan Valdman
Supervisor:
Department of Applied Mathematics
Synopsis:

This course provides a foundational overview of differential equations, starting with basic motivation and examples of ODEs and progressing to essential solution methods like separation of variables. Key theorems on existence and uniqueness establish when solutions can be guaranteed. Linear and system-based ODEs are covered with methods like characteristic polynomial analysis, followed by examples of non-linear models such as predator-prey and epidemiological models to showcase real-world applications. Finally, an introduction to partial differential equations (PDEs) extends these concepts to multi-variable contexts.

The course will also cover numerical methods for solving ODEs and PDEs, including implicit and explicit Euler methods, Runge-Kutta methods, and finite element methods for both ODEs and PDEs.

Requirements:

It is recommended to be comfortable with topics covered by BIE-LA1, BIE-MA1, and BIE-MA2 courses.

Syllabus of lectures:

1 Motivation and first examples of ordinary differential equations (ODEs)

2 Separation of variables

3 The Cauchy problem, theorems on the existence and uniqueness of solution

4 Linear ODEs

5 Systems of linear ODEs

6 Explicit and implicit Euler methods, stability domains

7 Runge-Kutta methods, applications to systems of ODEs

8 Examples of non-linear models (predator-prey model, epidemiological models)

9 Introduction to partial differential equations (PDEs)

10 Boundary value problems

11 Shooting method, finite differences, finite element method for ODEs

12 Finite element method for PDEs

Syllabus of tutorials:

1 Motivation and first examples of ordinary differential equations (ODEs)

2 Separation of variables

3 The Cauchy problem, theorems on the existence and uniqueness of solution

4 Linear ODEs

5 Systems of linear ODEs

6 Explicit and implicit Euler methods, stability domains

7 Runge-Kutta methods, applications to systems of ODEs

8 Examples of non-linear models (predator-prey model, epidemiological models)

9 Introduction to partial differential equations (PDEs)

10 Boundary value problems

11 Shooting method, finite differences, finite element method for ODEs

12 Finite element method for PDEs

Study Objective:
Study materials:

1. D. Schaeffer and J. Cain, Ordinary Differential Equations: Basics and Beyond, Springer-Verlag New York Inc., 2016

2. Braun M., Differential equations and their applications: An Introduction to Applied Mathematics, Spinger, 1992

3. L. C. Evans: Partial Differential Equations, 2nd ed., American Mathematical Society, Rhode Island, 2010.

Note:
Further information:
https://courses.fit.cvut.cz/BIE-DIF
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
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
roomTH:A-s135
Marchesiello A.
Bouchala O.
12:45–14:15
(lecture parallel1)
Thákurova 7 (budova FSv) roomTH:A-s135
Valdman J.
Marchesiello A.
14:30–16:00
(lecture parallel1
parallel nr.101)
Thákurova 7 (budova FSv)
Tue
Wed
Thu
Fri
The course is a part of the following study plans:
Data valid to 2025-01-22
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