- Code MATH2406
- Unit Value 6 units
- Offered by Department of Mathematics
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career UGRD
- Prof John Urbas
- Mode of delivery In Person
Second Semester 2014
See Future Offerings
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.
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.
- Assignments (30%; LO 1-4)
- Final exam (70%; LO 1-4)
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36 Lectures and tutorials by arrangement
Requisite and Incompatibility
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- Student Contribution Band:
- Unit value:
- 6 units
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- Domestic fee paying students
- International fee paying students
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|7450||21 Jul 2014||01 Aug 2014||31 Aug 2014||30 Oct 2014||In Person||N/A|