## MAS254 Computational and Numerical Methods

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

Semester 2, 2019/20 | 10 Credits | ||||

Lecturer: | Dr Gary Verth | Timetable | Reading List | ||

Aims | Outcomes | Teaching Methods | Assessment |

**Prerequisites:** MAS152 (Essential Mathematical Skills and Techniques); MAS253 (Mathematics for Engineering Modelling)

The following modules have this module as a prerequisite:

MAS340 | Mathematics (Computational Methods) |

## Outline syllabus

- Non-linear Algebraic Equations: Bisection, one-point iteration, Newton's method, secant method.
- Linear Algebraic equations: Gauss-Seidel method. Gaussian elimination, partial pivoting, LU decomposition.
- Eigenvalues: Power method for the dominant eigenvalue.
- Interpolation: Lagrange interpolation formula.
- Data Fitting: Least-squares polynomial approximation for linear and quadratic fitting.
- Numerical Differentiation and Integration: 3 point formulae for 1st and 2nd derivatives with errors. Trapezium rule, Simpson's rule
- Ordinary Differential Equations (initial value problems): First order: Runge-Kutta: Euler 1, 2, 3; classical 4th order Runge-Kutta. Adaptation to second and higher order equations.
- Ordinary Differential Equations (linear boundary value problems): Application to 2nd order equations of finite difference scheme using 3 point differentiation formulae.
- Linear Programming: Graphical methods.

## Aims

- To consolidate previous mathematical knowledge.
- To continue introducing students to mathematical and numerical techniques used in the area of Mechanical Engineering.

## Learning outcomes

At the end of the course the student should be able to:- use basic iteration techniques to solve a non-linear algebraic equation;
- apply iteration or direct methods to solve a system of linear equations;
- calculate the dominant eigenvalue of an eigenvalue problem;
- interpolate functions using the Lagrange interpolation formula;
- apply a least squares polynomial approximation to fit data;
- differentiate and integrate numerically;
- solve initial value problems for 1st and 2nd order ordinary differential equations;
- solve linear boundary value problems for 2nd order ordinary differential equations;
- solve linear programming problems using graphical methods.

## Teaching methods

Lectures, tutorials, problem solving

36 lectures, 9 tutorials

## Assessment

One two-hour written examination.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Atkinson, K.E. | Introduction to Numerical Analysis | Information Commons 518 (A) | Blackwells | Amazon |

B |
Burden, R.L. and Douglas Faires, J | Numerical Analysis | |||

B |
Gerald, C.F. and Wheatley P.O. | Applied Numerical Analysis | Western Bank Library 518 (G) | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.