The descriptions are for modules currently being taught. They should be viewed as an example of the modules we provide. All modules are subject to change for later academic years.

Numerical Analysis (NUMA) 2015/6

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

Module Prerequisites

Prerequisite knowledge

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

Workload

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

Private Study

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.

Assessment

Closed Assessment

  • Closed Exam Summer 5-7, 2.00 hours

Closed Assessment

  • Summer 5-7, 2.00 hours
Students will answer one compulsory question and two other questions from a choice of three.

Formative Feedback

4 hours of feedback sessions addressing exam-style questions.
5 hours of lab-based practical classes.

Description

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.

Aims

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

Learning Outcomes

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

Content

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.

Teaching Materials

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

Recommended 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
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Last updated: 19th September 2016