# ACM30220 Partial Differential Equations

This course provides a thorough introduction to the mathematical theory of partial differential equations both the classical theory of Laplace, Cauchy, Fourier, Gauss etc and more modern analytic developments. Topics include first order equations, Cauchy problems, characteristics, linear second-order equations, classification, boundary value problems for elliptic equations, perimeter and initial value problems for hyperbolic and parabolic equations, fundamental solutions, Green's functions, eigenfunction expansions, Fourier transforms, and maximum principles.

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Curricular information is subject to change

Learning Outcomes:

The student masters the basic principles and methods for the analysis of partial differential equations, including first-order equations, Cauchy's problems, characteristics, linear second-order equations, classification, boundary value problems for elliptic equations, boundary and initial value problems for hyperbolic and parabolic equations, fundamental solutions, maximum principles, Fourier series, and Fourier transform techniques. The student is then able to apply the techniques to study specific examples.

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24

Autonomous Student Learning

46

Lectures

30

Total

100

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry, and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Recommendations:

ACM20150 Vector and Integral Calculus

Module Requisites and Incompatibles
Incompatibles:
ACM30080 - PDEs in Financial Maths, ACM30120 - PDEs for Fin. Maths (online)

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Varies over semester Varies over the Trimester n/a Standard conversion grade scale 40% No

40

No
Examination: final examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

60

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour