This module aims to: To support Semester 6 modules by introducing Laplace Transforms and their use in solving linear differential equations.2. To deepen the students knowledge of geometry, by introducing the formulation and solution of 3D problems involving lines and planes in vector notation. To be able to calculate the divergence, gradient and curl and relate these to ideas in geometry and physics. 3. To use an iterative technique in several variables to solve systems of equations equations numerically and as an introduction to material they may cover in subsequent modules.
The Laplace Transform: Definition. The Laplace transform of common functions. Linearity rules. Transform of derivatives. Application: Solution of first and second order linear ODE’s with constant coefficients.
Vector Calculus: i, j, k notation. Equations of lines and planes in 3D. Intersection point of line with a plane. Gradient, divergence, curl. Directional derivatives and maximum rate of change. Tangent planes and normal lines to a surface. Jacobian for 2 variables, linear approximation.
Numerical Methods: Newton-Raphson in 2 variables to solve systems of equations numerically. Implement algorithm in Matlab.
