## MAS254 Computational and Numerical Methods

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.

## Timetable

Mon | 14:00 - 14:50 | lecture | Hicks Lecture Theatre 1 | ||||

Mon | 15:00 - 15:50 | tutorial | Hicks Lecture Theatre 1 | ||||

Fri | 11:00 - 11:50 | lecture | Diamond Building LT4 | ||||

Fri | 12:00 - 12:50 | tutorial | Diamond Building LT4 |