Many physical processes such as vibrating strings, diffusion of heat and fluid flows are well modelled by partial differential equations and/or integral equations. This course provides an introduction to methods for solving and analysing standard partial differential equations and integral equations, including an introduction to complex analytic techniques.
The course consists out of two main modules: Complex Analysis and Partial Differential Equations. Complex Analysis: differentiability; analytic continuation; conformal mapping; complex integration; Cauchy integral theorems; residue theorem; applications to real integration. Laplace transform: properties, Watson's lemma, the inversion integral, inversions involving residues and branch cuts, asymptotics, application to ODE's and PDE's Partial Differential Equations; classification of second order partial differential equations into elliptic, parabolic and hyperbolic types; elliptic equations; integral formulae, maximum principle; parabolic equations; diffusion; representation by a kernel (Green's functions); hyperbolic equations; d'Alembert solution and the method of characteristics; analytic methods; separation of variables; orthogonal expansions; Fourier series; Distributions, Transforms, Complex Analysis and applications; Distributions: definition, convergence of distributions, derivative. Fourier transform: definition, properties, application to Green's functions.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, students will have the knowledge and skills to:
1. Explain the fundamental concepts of partial differential equations and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of Fourier series, complex analysis and integral transform techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from partial differential equations and complex analysis
4. 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
- Assignments (30%; LO 1-4)
- Final exam (70%; LO 1-4)
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Workload
36 Lectures and tutorials by arrangement
Requisite and Incompatibility
Majors
Fees
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- 2
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course 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 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2015 | $3096 |
- International fee paying students
| Year | Fee |
|---|---|
| 2015 | $4146 |
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 |
|---|---|---|---|---|---|---|
| 1904 | 20 Jul 2015 | 07 Aug 2015 | 31 Aug 2015 | 30 Oct 2015 | In Person | N/A |
