MTH3011 · Partial differential equations

Overview

This unit covers exact and numerical solutions for partial differential equations of various types. Explicit solution methods include methods of characteristics, separation of variables, Fourier series and transform, fundamental solutions, etc. Some of these methods will be explored for linear, and possibly some non-linear, equations of elliptic, parabolic or hyperbolic types. Numerical analysis techniques (of finite difference, finite volume or finite element types) will be covered for some of these models, with an emphasis on establishing the robustness and accuracy (consistency) of the methods, for both stationary and time-dependent models.

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

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

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Solve a range of nonlinear partial differential equations using a variety of technique;
2. Appreciate the properties of multi-dimensional partial differential equations, including suitable initial and/or boundary conditions;
3. Demonstrate an understanding of the mathematical properties of inhomogeneous partial differential equations and solve them exactly under some simple conditions using in particular Duhamel’s principle;
4. Demonstrate an understanding of the principles of numerical analysis for ordinary and partial differential equations, including the stability and consistency analysis of the schemes;
5. Choose specific output formats for and interpret the results of numerical schemes for various models.

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.