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 … For more content click the Read More button below. 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.

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.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Kengo Deguchi

Unit Coordinator(s)

Dr Kengo Deguchi

Learning outcomes

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

Solve a range of nonlinear partial differential equations using a variety of technique;

Appreciate the properties of multi-dimensional partial differential equations, including suitable initial and/or boundary conditions;

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;

Demonstrate an understanding of the principles of numerical analysis for ordinary and partial differential equations, including the stability and consistency analysis of the schemes;

Choose specific output formats for and interpret the results of numerical schemes for various models.

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

Learning resources

Required resources

A First Course in the Numerical Analysis of Differential Equations by A. Iserlies, Cambridge, 1996.

Applied Partial Differential Equations by R. Haberman, Pearson, 2004.

Partial Differential Equations with Numerical Methods by S. Larsson & V. Thomas, Springer, 2005.

Tips on writing in mathematics http://www.stolaf.edu/people/zorn/prooftips.pdf <http://www.stolaf.edu/people/zorn/prooftips.pdf>

Writing mathematics well http://www.math.hmc.edu/~su/math-writing.pdf <http://www.math.hmc.edu/~su/math-writing.pdf>

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