Scientific Computing and Numerical Methods module (MA32005)

How do scientists, engineers, and mathematicians tackle complex problems like population growth, heat transfer, or planetary motion? These are the kinds of challenges that can’t be solved with simple equations. Instead, the answer lies in numerical methods.

This module introduces you to the world of scientific computing. Mathematics and coding come together to solve real-world problems.

You’ll learn how to use the specialist software MATLAB to tackle systems of equations, simulate physical systems, and approximate solutions to differential equations. Through practical exercises, you’ll build the tools needed to solve problems that don’t have neat textbook answers. You'll use methods like root-finding, spline interpolation, Monte Carlo techniques, predictor-corrector schemes, and finite difference approaches.  

This module gives you essential skills that are in high demand across science, engineering, data science, and finance. You’ll gain hands-on experience in translating mathematical ideas into working code. You will enhance your ability to model, simulate, and interpret complex systems. 

What you will learn

In this module, you will:

• use MATLAB to implement numerical methods and solve applied problems
• apply predictor-corrector and finite difference methods to differential equations
• explore Monte Carlo simulations and random walk models
• use interpolation and root-finding techniques to work with real data

By the end of this module, you will be able to:

• translate mathematical problems into computational algorithms
• convert differential equations into systems of linear equations and solve them using matrix algebra
• apply numerical techniques to model and analyse physical or data-driven systems
• write clean, well-documented MATLAB code to support your analysis

Assignments / assessment

• Coursework (40%) – programming-based assignments using MATLAB
• Final exam, two hours (60%) – programming-based exam implementing numerical methods

Teaching methods / timetable

You will learn through lectures covering the mathematics behind numerical methods, and IT workshops where you will produce your own code to implement numerical methods and solve real-world problems.