Monash University Handbook

This unit introduces mathematical techniques for differential equations. These equations appear in a number of physical models, such as oscillations, heat conduction and transport equations. Methods to study ordinary differential equations include separation of variables, substituting methods, variation of parameters, series solutions and numerical techniques (Euler, Heun's method). Partial differential equations describing physical models are derived, and analysed through Fourier series, separation of variables and characteristics techniques.

Outcomes

On completion of this unit students will be able to:

Describe various classes of ordinary and partial differential equations and the physical systems to which they apply;
Identify the differential equations that describe various physical processes including those for simple harmonic motion, diffusion, wave propagation and mass transport;
Describe the essential mathematical properties of these differential equations;
Construct solutions of differential equations using analytic and computational methods;
Appreciate the role that differential equations and their solutions play in the scientific process, in particular their use as a tool to model physical systems and allow predictions to be made and tested.