In Stage 1 and Stage 2, students frequently apply analytical methods to physical problem solving. This module provides a foundation in numerical approximations to analytical methods – these techniques are essential for solving problems by computer. The following topics are covered: Linear equations, zeros and roots, least squares & linear regression, eigenvalues and eigenvectors, errors and finite differences, linear programming, interpolation and plotting functions, numerical integration, , numerical differentiation, solutions to ordinary differential equations using numerical methods.
This module appears in:
- Physical Sciences Stage 2/3/4
- STMS Undergradute Stage 2 & 3
20 hours of lectures and 12 hours of computer console sessions.
This module is expected to occupy 150 total study hours, including contact hours.
This is not available as a wild module.
Method of assessment
40% coursework: 6 problem sheets involving handwritten and computer programming components; 60% final exam.
C. Moler, Numerical Computing with MATLAB, Society for Industrial and Applied Mathematics, SIAM, 2004 ISBN 978-0-898715-60-6S. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, 2008. ISBN: 978-0-07-313290-7
See the library reading list for this module (Canterbury)
Knowledge and understanding of:Physical laws and principles, and their application to diverse areas of physics.
An ability to identify relevant principles and laws when dealing with problems, and to make approximations necessary to obtain solutions.
An ability to solve problems in physics using appropriate mathematical tools.
An ability to use mathematical techniques and analysis to model physical behaviour.
An ability to solve advanced problems in physics using appropriate mathematical tools, to translate problems into mathematical statements and apply their knowledge to obtain order of magnitude or more precise solutions as appropriate.
An ability to interpret mathematical descriptions of physical phenomena.
A working knowledge of a variety of mathematical and/or computational techniques applicable to current research within physics.
Competent use of appropriate C&IT packages/systems for the analysis of data and the retrieval of appropriate information.
An ability to present and interpret information graphically.
An ability to make use of appropriate texts, or other learning resources as part of managing their own learning.
Problem-solving skills - in the context of both problems with well-defined solutions and open-ended problems; an ability to formulate problems in precise terms and to identify key issues, and the confidence to try different approaches in order to make progress on challenging problems. Numeracy is subsumed within this area.
Analytical skills – associated with the need to pay attention to detail and to develop an ability to manipulate precise and intricate ideas, to construct logical arguments and to use technical language correctly.