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 explains its connection to the diffusion equation. Fourier methods (both series and transforms) are used to treat 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 can explore the properties of dynamical systems. Although you will be required to use Maxima in some of the assignments, it is possible to complete the module without extensive use of this package. There will be plenty of optional exercises that illustrate the power of computers for exploring the properties of dynamical systems.
The full content list is on the Open mathematics and statistics website.
Understanding how to analyse dynamical processes is a central competence for using mathematics in science, engineering, and economics. Mastering the material in this module will give you powerful tools used by practising applied mathematicians.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
We’re using a new examination verification process for this module. We may ask you to attend a 15-minute post-exam video discussion, where you’ll present a photo ID and discuss your answers to a small number of questions with a tutor or member of the module team. The discussion isn’t graded; it’s only to verify that you completed the exam yourself.
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
You can study this module on its own or use the credits you gain towards an Open University qualification.
MS327 is an option module in our:
Deterministic and stochastic dynamics (MS327) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2031.
As a student of The Open University, you should be aware of the content of the academic regulations, which are available on our Student Policies and Regulations website.
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There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
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