The first aim of this course is to reinforce the student’s competence in a range ofmathematical 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 thesolution of engineering problems, such as the analysis of system behaviour.
Signals
Classification of signals. Piecewise linear signals. Waves. Trigonometric equations and identities. Periodic signals. Even and odd signals.
Applications of Calculus
Review of differentiation. Integration techniques and improper integration. Using integration to solve linear differential equations. Partial differentiation. Scalar fields. Gradient of a scalar field. Directional derivatives and maximum rate of change. Vector fields. Divergence and Curl of a vector field.
The Laplace Transform
Definition of the Laplace Transform and simple examples. Existence of theLaplace Transform. Table of Laplace Transforms of common functions. Linearityof the Laplace Transform. Laplace Transforms of unit step and unit impulsefunctions. Inverting Laplace Transforms – use of partial fractions. Shifttheorems. Laplace Transform method for first order linear ODE’s with constantcoefficients. Laplace Transform Method for second order linear ODE’s withconstant coefficients (e.g. RLC systems). Transfer functions, feedback, and stability.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |