Introductory description

FP041-15 Scientific Programming and Mathematical Modelling

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

What is a mathematical model?

• Different types of models
• The modelling cycle
• Making assumptions and simplifications
• Making predictions
• Understanding limitations

Basics of programming in Python

• What is a computer program?
• Introduction to the Python programming language
• Variables and Data Types
• Conditional Statements
• Repetition
• Functions and Recursions

Basics of Latex

• What is Latex?
• Using different latex document classes
• Understanding latex syntax
• Working with different latex environments

Numerical Methods

• Location of roots of f(x) = 0 by consideration of changes of sign
• Approximate solution of equations using Newton-Raphson and simple iterative methods of the form x_{n+1} = f(x_n)
• Numerical approximations of integrals using the trapezium rule.

Linear programming

• Formulation of problems as linear programs
• Graphical solutions of two variable problems
• The Simplex algorithm and tableau for optimising problems

Modelling classical mechanical systems

• Kinematics in 1D and 2D
• Dynamics in 1D and 2D

Modelling the spread of a disease

• Exponential growth and decay
• Differential equations for population growth
• Differential equations for the spread of disease

Learning outcomes

By the end of the module, students should be able to:

• Take a real-life problem and, making the necessary assumptions, translate it into a mathematical model;
• Formulate mathematical problems, identify suitable algorithms to solve them, and implement them in a program written in a suitable programming language;
• Interpret and evaluate the outputs of a mathematical model in the context of the original situation
• Demonstrate that a mathematical model can be refined by considering its outputs and simplifying assumptions.

Indicative reading list

Bender, E.A., 2012. An introduction to mathematical modeling. Courier Corporation.

Hill, C., 2016. Learning scientific programming with Python. Cambridge University Press.

Langtangen, H.P. and Langtangen, H.P., 2009. A primer on scientific programming with Python (Vol. 2). Berlin, Germany: Springer.

Meerschaert, M.M., 2013. Mathematical modeling. Academic press.

View reading list on Talis Aspire

Subject specific skills

Mathematical Skills

Analytical Skills

Problem-solving skills

Investigative Skills

IT Skills

Transferable skills

Mathematical Skills

Analytical Skills

Problem-solving skills

Communication Skills

Investigative Skills

IT Skills