Unit information: Computational Mathematics in 2012/13

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	Dr. Tourigny
Open unit status	Not open
Pre-requisites	None
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Computational Mathematics provides an introduction to the rudiments of computer programming in a mathematical context, and uses the PYTHON language 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 16-20: 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.

Intended Learning Outcomes

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

Teaching Information

A mixture of lectures and practical sessions in the computer laboratory, with regular worksheets.

Assessment Information

The final assessment mark for the unit will be computed from the marks for 3 tests, equally weighted, to be completed during the practical sessions (50 min). Each test will consist of questions on the material taught so far.

Reading and References

• 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)