The module covers, at an intermediate level, further methods of linear algebra; further methods of differential and integral calculus; solutions of differential equations; statistical methods; Laplace transforms and their use; and the use of numerical methods as required by building services engineering students.
Methods of Linear Algebra
Gaussian elimination and the Gauss-Jordan methods and the Gauss-Seidel method.
Calculus
Properties of hyperbolic functions. Differentiation in parametric form. Curvature. Critical points of a function of several independent variables. Line integrals.
Ordinary Differential Equations
Analytical solution of first order differential equations and second order linear homogeneous and non-homogeneous differential equations with constant coefficients.
Laplace transforms
Properties of the Laplace transform and use of tables in the evaluation of Laplace transforms and inverse Laplace transforms. Application to differential equations.
Numerical methods
Numerical solution of first order differential equations including the fourth order Runge-Kutta method.
Statistics
Sampling and estimation. Control charts. Significance tests. Correlation and regression.
