The aim of the module is to enhance your mathematical knowledge and confidence in preparation for the demanding applications of the final stage modules, and a possible research career involving engineering science. You will develop an understanding of the numerical techniques used within modern Finite Element Analysis computer packages and develop an understanding of the mathematical basis of many of the advanced systems of equations governing engineering problems.
Number systems, errors and mathematical preliminaries,
Non-linear equations - Newton's method
Interpolation and Approximation - Lagrange, cubic spline, least squares
Numerical Differentiation and Integration - Euler's method, Trapezoidal and Simpson's rule, Gauss Quadrature.
Systems of linear and non-linear equations
Ordinary Differential Equations - Euler's and Runge Kutta method
Vector differential calculus
Vector integral calculus
Stokes’ theorem and Gauss’ divergence theorems
Three-dimensional cylindrical and spherical co-ordinates
Classification of partial differential equations
Solution of a range of differential equations of engineering importance