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 Open mathematics and statistics website.
Vocational relevance
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.
Entry
You must have passed one of the following:
You can check you’re ready for MS327 and see the topics it covers here.
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.
Study materials
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.
Teaching and assessment
Support from your tutor
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
- marking your assignments and offering detailed feedback to help you improve
- providing individual guidance, whether that’s for general study skills or specific module content
- guiding you to additional learning resources
- facilitating online discussions between your fellow students in the dedicated module and tutor group forums.
Online tutorials run throughout the module. Where possible, we’ll make recordings available. While they’re not compulsory, we strongly encourage you to participate.
Assessment
The assessment details for this module can be found in the facts box.
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.