| Unit name | Computational Mathematics |
|---|---|
| Unit code | MATH12001 |
| Credit points | 10 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Mezzadri |
| Open unit status | Not open |
| Pre-requisites |
A Level Mathematics |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Computational Mathematics provides an introduction to the rudiments of computer simulations in a mathematical context, and uses Matlab to illustrate some generic features. It also introduces symbolic computing via the software package MAPLE. Applications to other mathematics units will be stressed throughout.
Aims:
The aim of the unit is to introduce some of the concepts and techniques of computing that are useful in mathematical work. Two of the main topics considered are: 1.numerical simulations in Matlab; 2.the use and scope of symbolic computation packages.
Syllabus
Lecture 1: Introduction - History of computing
Lectures 2-3: Brief introduction to Matlab: - floating point arithmetic; - machine precision; - what can go wrong - examples.
Lectures 4-7: More matlab and basic programming: - the concept of variable in mathematics and computing; - vector and matrix manipulation in matlab; - discretization, plots; - recurrence relations, if-then-else constructions and boolean variables; - functions in matlab; - how to code elementary problems.
Lectures: 8-15: Basic ideas of numerical methods: - numerical integration: midpoint formula, trapezoidal formula,Simpson formula; - nonlinear functions: the bisection method (Newton-Raphson in 1d, time permitting); - LU factorisation and Gaussian elimination (only examples of 2x2 and 3x3 systems) - elementary ODE solving: Euler methods.
Lectures 16-22: Maple and symbolic computing
Relation to Other Units
Frequent use of material covered in the units Linear Algebra and Calculus will be made in order to motivate and illustrate the concepts.
The students will understand what computers do, have proficiency with Matlab. They will be introduced to simple numerical algorithms. They will learn to use MAPLE as an interactive and programming tool.
Transferable Skills:
Problem solving, programming, general IT skills.
A mixture of lectures and practical sessions in the computer laboratory, with regular worksheets and weekly homework.
The final assessment mark for the unit will be computed from the marks for 2 online tests. Each test will consist of questions on the material taught so far.
- Essential MATLAB for engineers and scientists / Brian Hahn, Dan Valentine. - Scientific Computing with MATLAB and Octave, Quarteroni/Saleri (electronic copy) - Maple and Mathematica: a problem solving approach for mathematics. Shingareva and Lizarraga-Celaya (electronic copy)
