MA5020 - Computational Mathematics (2024/25)
| Module specification | Module approved to run in 2024/25 | ||||||||||||||||
| Module title | Computational Mathematics | ||||||||||||||||
| Module level | Intermediate (05) | ||||||||||||||||
| Credit rating for module | 30 | ||||||||||||||||
| School | School of Computing and Digital Media | ||||||||||||||||
| Total study hours | 300 | ||||||||||||||||
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| Running in 2024/25(Please note that module timeslots are subject to change) | No instances running in the year |
Module summary
This module enables the student to further develop and apply numerical techniques to a range of problems including the solution of ordinary differential equations related to both physical and financial/economic models.
This module enables the student to further develop and apply numerical techniques to a range of problems including the solution of ordinary differential equations related to both physical and financial/economic models.
The aims are:
To enable students to apply approximation techniques to problems of both theoretical and practical importance and understand the cause of and interpret the degree of error involved.
To prepare students with the tools necessary for solving a range of problems in situations suitably described by ordinary differential equations and by difference equations.
To understand modelling with linear and nonlinear dynamical systems and iterative methods of solution.
To enable students to understand and manipulate coded programmes for software packages such as Maple for solving larger problems.
To develop students’ knowledge, confidence and problem-solving skills leading to further academic progression and future employability in this area.
Prior learning requirements
None.
Available for Study Abroad? NO
Syllabus
Iterative methods for approximating solutions of systems of linear equations. (LO3-4)
Initial Value Problems - Euler and Trapezium methods. (LO1)
Linear Multistep Methods with Maple. (LO1,4,5)
Predictor-Corrector Methods. (LO1)
Numerical approximations to Two-point Boundary Value problems. (LO2)
Discrete Dynamical Systems and Difference Equations. (LO3)
Balance of independent study and scheduled teaching activity
This module will be delivered through a mixture of lectures, tutorials and laboratory workshops.
Students will be expected to spend some time on unsupervised work, for example, private study of problem sheets and on the preparation of coursework, test and examination.
Lecture notes and links to useful resources will be available on the module website (WebLearn) and can be accessed at any time. The module website will also be used as an additional medium of communication between the module teaching team and the students.
Learning outcomes
On successful completion of this module, students should be able to:
LO1. Understand and implement numerical methods to approximate the solutions of initial value problems and implement simple predictor-corrector methods.
LO2. Obtain numerical approximations to the solutions to certain boundary value problems.
LO3. Understand discrete dynamical systems and their application in modelling problems in natural sciences, engineering and finance.
LO4. Appreciate the limitations of the methods and be able to evaluate the feasibility of solutions, use appropriate software, analyse and interpret the results.
LO5. Critically evaluate and reflect on their learning, development and achievements within the Context of computational mathematics.
Bibliography
Core Text:
Burden, R.L. and J. Douglas Faires, Thomson (latest ed.) Numerical Analysis,
Recommended Reading:
Sandefur, J. ( 1990),Discrete Dynamical Systems Theory and Applications, T, Oxford.
Maple 13- Introductory Programming Guide, Maplesoft, 2009.
On-line sources: