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 … For more content click the Read More button below.

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.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Kengo Deguchi

Unit Coordinator(s)

Dr Kengo Deguchi

Notes

This Level 4 unit and its Level 3 counterpart MTH3011 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, more challenging assessment tasks, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

On successful completion of this unit, you should be able to:

Utilise and integrate cutting-edge methodologies to solve a diverse range of linear and nonlinear partial differential equations;

Conduct a comprehensive critical evaluation of the characteristics of multi-dimensional partial differential equations, including the implementation and justification of initial and boundary conditions

Exhibit a deep understanding of the mathematical properties of inhomogeneous partial differential equations and formulate exact solutions under complex specified conditions

Critically analyse and synthesise the concept of well-posedness for diverse boundary value problems and initial value problems;

Demonstrate and apply the indispensability of functional analysis for the advanced analysis of partial differential equations by exploring and solving elliptic equations;

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

Workload requirements

Workload

Off campus attendance requirements

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.

Miscellaneous items required (unit course reader, printing, stationery) - $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics