MTH4015 Partial differential equations
Faculty of Science
MTH4015 Partial differential equations is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2025 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2025
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
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Requisites
Before MTH4015
No prerequisites or corequisites besides the enrolment rules below.
After MTH4015
No unit lists MTH4015 as a prerequisite in the 2025 handbook.
Enrolment rules
PREREQUISTE: You must have passed one unit from MTH2010 or MTH2015 or ENG2005 and one unit from MTH2032 or MTH2040, or be enrolled in the Master of Mathematics or the Master of Financial Mathematics.
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.
Offerings in 2025
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Learning outcomes
When you finish this unit, you should be able to:
- 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 and teaching
- Applied sessions22 hours
- Seminars36 hours
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
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. Larss
Contacts
- Chief Examiners
- Dr Kengo Deguchi
- Unit Coordinators
- Dr Kengo Deguchi
Common questions
What are the prerequisites for MTH4015?
MTH4015 has no prerequisites, but enrolment rules apply.
When is MTH4015 offered?
In 2025, MTH4015 runs in Semester 1 at Clayton.
Does MTH4015 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.