MTH4015 · Partial differential equations

Overview

This unit covers various analytic methods for partial differential equations. Explicit solution methods include separation of variables, Fourier series and transforms, fundamental solutions, and more. These methods will be explored for linear and nonlinear equations of elliptic, parabolic, or hyperbolic types. Abstract analysis techniques will also be covered for some of these partial differential equations, with an emphasis on establishing well-posedness for both stationary and time-dependent partial differential equations, and introducing basic concepts in functional analysis.

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. Utilise and integrate cutting-edge methodologies to solve a diverse range of linear and nonlinear partial differential equations;
2. Conduct a comprehensive critical evaluation of the characteristics of multi-dimensional partial differential equations, including the implementation and justification of initial and boundary conditions
3. Exhibit a deep understanding of the mathematical properties of inhomogeneous partial differential equations and formulate exact solutions under complex specified conditions
4. Critically analyse and synthesise the concept of well-posedness for diverse boundary value problems and initial value problems;
5. Demonstrate and apply the indispensability of functional analysis for the advanced analysis of partial differential equations by exploring and solving elliptic equations;

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.