Deterministic and stochastic dynamics
Qualification dates
| Start |
End |
|
|
This module is an accessible introduction to the study of applied mathematics at OU level 3. It introduces core topics in applied mathematics at this level and is structured around three books: Fundamental concepts of dynamics, Deterministic dynamics and Stochastic processes and diffusion. As well as using traditional pen-and-paper mathematics, the module uses the Maxima computer algebra system to illustrate and explore the properties of dynamical systems.
What you will study
This module is presented as three books.
Book 1: Fundamental concepts of dynamics
The first book considers ordinary differential equations, Newton’s second law, conservation of energy, and the concepts of fixed point, limit cycles and constants of motion. It also introduces a framework for discussing random processes, such as random walks.
Book 2: Deterministic dynamics
The second book develops some more advanced concepts. In the case of conservative systems, it introduces the calculus of variations and develops Lagrangian dynamics from Hamilton’s principle. In the case of dissipative systems, it uses the concepts of maps to model dynamical processes. ‘Chaos’ is defined and explored using the strange attractor. The book introduces the notions of Lyapunov exponents, fractal dimensions of attractors, and their connection via the ‘Lyapunov dimension’ formula.
Book 3: Stochastic processes and diffusion
The third book investigates the random walk as the archetypical random dynamical process, and explain its connection to the diffusion equation. Fourier methods (both series and transforms) are used in the treatment of the diffusion equation and probability theory. The module concludes with a look at some further applications of random dynamical systems, including models used for option pricing in mathematical finance.
The module uses the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. You will be required to use Maxima in some of the assignments, but it is possible to complete the module without an extensive use of this package. However, there will be plenty of optional exercises which illustrate the power of computers for exploring the properties of dynamical systems.
You can find the full content list on the .
Entry requirements
You must have passed one of the following:
You can .
Preparatory work
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz and follow the advice in the quiz.
The key topics to revise include:
- differential equations
- mechanics.
What's included
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials
- audio and video content
- Maxima algebra software and associated guidance
- assessment details, instructions and guidance
- online tutorial access
- access to student and tutor group forums.
You’ll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You’ll also receive a printed module handbook.
You will need
A scientific calculator.
Computing requirements
- Primary device – A desktop or laptop computer. It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device.
- Peripheral device – Headphones/earphones with a built-in microphone for online tutorials.
- Our OU Study app operates on supported versions of Android and iOS.
- Operating systems – Windows 11 or latest supported macOS. Microsoft will no longer support Windows 10 as of 14 October 2025.
- Internet access – Broadband or mobile connection.
- Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable.