• Offered by Mathematical Sciences Institute
  • ANU College ANU Joint Colleges of Science
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career PGRD
  • Course convener
    • Prof Xu-Jia Wang
  • Mode of delivery In Person
  • Co-taught Course
  • Offered in Second Semester 2023
    See Future Offerings
  • STEM Course

The course will discuss the three main classes of equations, elliptic, parabolic and hyperbolic. It is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.

Topics to be covered will include fundamental solutions, maximum principles, regularity (smoothness) of solutions, variational problems, Holder and Sobolev spaces.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

  1. Explain the concepts and language of partial differential equations and their role in modern mathematics and applied contexts.
  2. Analyse and solve complex problems using partial differential equations as functional and analytical tools.
  3. Apply problem-solving with partial differential equations to diverse situations in physics, engineering and other mathematical contexts.
  4. Conduct some (limited) independent research under expert supervision.

Indicative Assessment

  1. 3-4 written assignments involving problem-solving, proofs of theorems and extension of theory (75) [LO 1,2,3,4]
  2. Final exam (25) [LO 1,2,3]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.


The expected workload will consist of approximately 130 hours throughout the semester including:

Face-to-face component which may consist of 3 x 12 hours (36 hours total) of lectures.

Approximately 94 hours of self-directed study which will include preparation for lectures, tutorials and other assessment tasks.  

The exact workload distribution will vary from year to year.

Inherent Requirements

Semester 2 in 2023-25

Requisite and Incompatibility

To enrol in this course you need to be enroled in the Master of Science in Mathematical Sciences, Master of Mathematical Sciences (Advanced), the Master of Science in Astronomy and Astrophysics, or the Master of Science in Astronomy and Astrophysics (Advanced) and must have completed either MATH3320 with a mark of 60 or above or MATH6212 with a mark of 60 or above (or their equivalent). Incompatible with MATH6202 and MATH4202.

Prescribed Texts

Partial Differential Equations, by Lawrence C. Evans.

Preliminary Reading

Chapters 2, 5, 6, 7, 8 of the above book.


Tuition fees are for the academic year indicated at the top of the page.  

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

6.00 0.12500
Domestic fee paying students
Year Fee
2023 $4320
International fee paying students
Year Fee
2023 $6180
Note: Please note that fee information is for current year only.

Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
7533 24 Jul 2023 31 Jul 2023 31 Aug 2023 27 Oct 2023 In Person N/A

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