FP041-15 Scientific Programming and Mathematical Modelling
Introductory description
FP041-15 Scientific Programming and Mathematical Modelling
Module aims
To develop an understanding of the basic principles of mathematical models and demonstrate basic competence in computer programming.
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
Study time
| Type | Required |
|---|---|
| Lectures | 10 sessions of 1 hour (7%) |
| Seminars | 10 sessions of 1 hour (7%) |
| Practical classes | 10 sessions of 2 hours (13%) |
| Private study | 110 hours (73%) |
| Total | 150 hours |
Private study description
Private Study.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group A1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
Assessment component |
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| Written portfolio | 80% | Yes (extension) | |
Reassessment component is the same |
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Assessment component |
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| Individual Presentation | 20% | Yes (extension) | |
Reassessment component is the same |
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Feedback on assessment
Written feedback provided on Tabula
Courses
This module is Core for:
- Year 1 of FIOE Warwick International Foundation Programme