Aims

To reinforce the computing in Python studied at Stage 1, and to move towards expectations of more independent programming. To introduce a wider range of mathematical techniques within Python, including methods that will be useful towards future project work.


Module Summary

Computing methods are of great use in a wide range of applications applied mathematics. This module builds on the methods introduced at Stage 1, introducing additional techniques, some of increasing mathematical and computational sophistication. In implementing these methods, students will attain increasing competence with mathematical computing, and an increasing ability to use such methods independently, towards project-orientated goals.

Outline Of Syllabus

⦁       Advanced plotting, including surfaces, vector fields and trajectories.

⦁       Curve fitting (e.g. least squares fitting of known function to data).

⦁       Root finding (e.g. Newton-Raphson and Python solvers).

⦁       Numerical derivatives through finite difference, and related techniques of numerical integration.

⦁       Numerical solution of ordinary differential equations (e.g. Euler, Runge-Kutta and Python solvers)

* Finite difference methods for numerical solutions of partial differential equations.

⦁       Use Python for matrix manipulation, linear algebra and related techniques.

* Applications of numerical methods to dynamical systems in applied mathematics.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures and problem classes are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving generqala feedback on marked work. Practicals are used to help develop the students' ability at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

The coursework assignment allows the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as a primary summative purpose.