In physics, economics and engineering, we frequently encounter quantities (for example energy) that depend on many variables (such as position, velocity, temperature). Usually, this dependency is expressed through a partial differential equation, and solving these equations is important for understanding these complex relationships.
In this course, we will study first- and second-order partial differential equations. The solution methods studied in this course will include the method of characteristics, separation of variables, Fourier series and Fourier transforms.
This course will be useful for majors in economics, mathematical finance, engineering and physics. We will illustrate the theory with examples from these disciplines.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of partial differential equations and their role in modern mathematics and applied contexts
- Demonstrate accurate and efficient use of Fourier series, complex analysis and integral transform techniques
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from partial differential equations and complex analysis
- Apply problem-solving using Fourier series, complex analysis and integral transform techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Indicative Assessment
- Mid-semester exam (20) [LO 1,2,3,4]
- Workshop presentations (10) [LO 1,2,3,4]
- Regular Assignments - weekly or once every two weeks (30) [LO 1,2,3,4]
- Final exam (40) [LO 1,2,3,4]
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Workload
The expected workload will consist of approximately 130 hours throughout the semester as follows:
• Face-to-face component which will consist of 4x1 hours lectures per week (approximately 48 hours total) and 1x1 hour workshop for 10 weeks (10 hours).
• Approximately 72 hours of self-directed study which will include preparation for lectures, workshops, assignments, and exams.
Inherent Requirements
No specific inherent requirements have been identified for this course.
Requisite and Incompatibility
Prescribed Texts
None, unless specified in the class summary.
Preliminary Reading
The lecture materials provide a self-contained account of the material. Students who want additional resources will find a number of relevant texts available in ebook format through the ANU library.
Assumed Knowledge
It is recommended that students have completed MATH2305 with a mark of at least 60. Students who have successfully completed MATH2305 with a mark of 50-59 are advised to seek advice from the MATH2306 course convener before enrolling in the course.
Fees
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:
- 1
- 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.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
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.
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 |
|---|---|---|---|---|---|---|
| 7538 | 27 Jul 2026 | 03 Aug 2026 | 31 Aug 2026 | 30 Oct 2026 | In Person | N/A |