MTH2032 · Differential equations with modelling

Overview

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.

Areas of study: Applied mathematics Astrophysics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics Physics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Describe various classes of ordinary and partial differential equations and the physical systems to which they apply;
2. Identify the differential equations that describe various physical processes including those for simple harmonic motion, diffusion, wave propagation and mass transport;
3. Describe the essential mathematical properties of these differential equations;
4. Construct solutions of differential equations using analytic and computational methods;
5. 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.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.