The first aim of Mathematics 5 is to reinforce the student’s competence in a range of mathematical techniques to support the analytical content of other modules in the course. The second aim is to enable the student to apply these mathematical techniques to the solution of engineering problems, such as the analysis of system behaviour and solution of control problems.
First Order Ordinary Differential Equations
Separable First-Order. General and particular solutions. Initial conditions. Existence and uniqueness of solutions. Classification of ODE’s. Integrating factor method for first order linear ODEs.
Second Order Ordinary Differential Equations
Modelling oscillation and circuits by second order ODE’s. Complementary function.Transient and steady state solutions. Free, damped and forced oscillation. Beats and resonance. Applications to circuits and motion with resistance proportional to speed.
The Laplace Transform:
Definition and simple examples. Existence of the Laplace Transform. Table of Laplace Transforms of common functions. Linearity of the Laplace Transform. Laplace Transform of unit step function. Inverting Laplace Transforms – use of partial fractions. Shift theorems. Laplace Transform method for first order linear ODE’s with constant coefficients and systems of first order linear ODE’s with constant coefficients. Laplace Transform Method for Second Order Linear ODE’s with constant coefficients.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |