This module equips students with mathematical tools essential for biomedical design and future lifelong mathematics learning, focusing on Laplace and Z Transform Methods for the solution of a variety of problems in analogue and digital systems. Learners will see the wide variety of engineering problems that can be tackled with these techniques, particularly problems in control. The student will also use a variety of software tools to solve, visualize and experiment with engineering problems applying these techniques.
1. Definition of the Laplace Transform, find and invert Laplace transforms using a standard table, linearity and shift theorems. Invert a Laplace transform by partial fraction techniques.
2. Solve first and second order linear differential equations with constant coefficients using the Laplace transform method.
3. Interpret the solutions of differential equation models of engineering systems appropriately, including control and the transfer function of a system, heating/cooling materials, exponential decay/growth, gas mixing, compartment model, dynamics and oscillations.
4. Definition of the Z transform, find and invert Z transforms using a standard table, linearity, shift theorems. Invert a Z transform by partial fraction techniques.
5. Define the transfer function of a linear digital system. Solve first and second order linear difference equations with constant coefficients using the Z transform method.
