School of Mathematics and Statistics (SoMaS)

MAS254 Computational and Numerical Methods

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

The following modules have this module as a prerequisite:

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

• 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

Assessment

One two-hour written examination.

Reading list