Workload - Private Study - Assessment - Description - Aims - Learning Outcomes - Content - Teaching Materials - Recommended Books

Module Code | COM00006C |
---|---|

Lecturers | Richard Wilson |

Taken By | CS 1, CSESE 1, CSYS 1, MEng CS 1, MEng CSAI 1, MEng CSESE 1, MEng CSYS 1 |

Number of Credits | 10 |

Teaching | Spring 2-10, Summer 1-4 |

Closed Assessment | [100%] Closed Exam Summer 5-7, 2.00 hours |

Reassessment |
[100%]
Closed Exam - August Resit Week, 2.00 hours |

Knowledge of A-level mathematics or equivalent will be assumed.

- Lectures: 12 x 1hr
- Software Labs: 5 x 1hr
- Problem Classes: 4 x 0.5hrs
- Private Study: 1hr
- Assessment: 2 x 1hr

In addition to study of the lecture material and course textbooks, students will be expected to spend approximately 8 hours preparing answers for the problem classes.

- Closed Exam Summer 5-7, 2.00 hours

Closed Assessment

- Summer 5-7, 2.00 hours

4 hours of feedback sessions addressing exam-style questions.

5 hours of lab-based practical classes.

This module covers the core techniques for solving numerical problems by computer. The particular problems addressed in this course are the solution of linear and non-linear equations both with and without constraints, fitting functions to data, and the optimisation of functions. The course will begin with some foundational mathematics, and then discuss the mathematical basis of the techniques. Students will then be able to create practical implementations of these methods in the lab classes.

The aims of this module are to:

- Introduce the main theories and methods in Computational Mathematics
- Illustrate the application of computational techniques in Numerical Analysis

On completion of the module, student will:

* Have a working knowledge of basic mathematical techniques in series, differentiation and linear algebra

* Understand how to use bisection, fixed point iteration and Newton's method to solve non-linear equations

* Know how to solve linear equations both with and without constraints

* Be able to apply Least-Squares to fit a function to data

* Understand how to optimise multivariate functions

Series; Maclaurin, Taylor, common series for functions. Vectors; scalar product. Linear algebra; matrices, special matrices, determinant, inverse, eigenvalues, decomposition, linear operators. Partial differentiation; small increments, extrema of multivariate functions.

Fixed point iteration; Bisection; Newton's method; Fitting data; models, least squares. Simultaneous linear equations; matrix representation, Gaussian elimination, approximate solution, constrained solution. Optimisation of multivariate functions.

Lecture notes will be provided online.

Other notes will also be provided online to supplement the materials in books.

Rating | Author | Title | Publisher | Year |
---|---|---|---|---|

**** | K. A. Stroud | Engineering Mathematics | Palgrave Macmillan | 2001 |

+++ | Chapra and Canale | Numerical Methods for Engineers | McGraw-Hill Higher Education | 2002 |

Last updated: 19^{th} September 2016