Mathematics and Computing 2

Overview

Linear Algebra: Gaussian elimination, eigenvalues and eigenvectors, iterative methods – Jacobi, Gauss-Seidel; Ordinary Differential Equations: Runge-Kutta method; Partial Differentiation; Partial Differential Equations: analytical and numerical solutions for heat, wave and Laplace’s equation, finite differences; Multiple Integrals: moment of inertia; Optimisation: linear programming, Simplex method, non-linear optimisation, steepest descent; Vector Calculus: scalar and vector fields, grad, div, curl, circulation, vorticity, Gauss’s divergence theorem; Statistics: normal distribution, hypothesis testing, confidence interval, test for difference between means, test for proportion, t-distribution; Introduction to Excel: matrix operations, solution of equations – inverse matrix and iterative methods, Runge-Kutta method, finite difference method, optimisation; Introduction to Visual Basic: functions / IF statements, loops and debugging, arrays, strings, functions, files.

Learning Objectives

Apply knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Some of the knowledge will be at the forefront of the particular subject of study.

Analyse complex problems to reach substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles.

Select and apply appropriate computational and analytical techniques to model complex problems, recognising the limitations of the techniques employed.

Skills

Analyse data using appropriate techniques.

Demonstrate analytical and problem-solving skills.

Support previously identified areas by using appropriate IT resources.

Assessment

None.