# Partial Differential Equations

University of Queensland

## Course Description

• ### Course Name

Partial Differential Equations

• ### Host University

University of Queensland

• ### Location

Brisbane, Australia

Mathematics

• ### Language Level

Taught In English

• ### Prerequisites

(MATH2000 or MP212 or 282 or MT250) + (MATH2100 or MP213 or 253)

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

2
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course Description
Review of separation of variables; classification of second equations; maximum principles for elliptic & parabolic equations. Green's functions & Neumann problem for Laplace & heat equations. Cauchy problem for heat & wave equations; non-linear boundary value problems: successive approximation; contraction principle.

Course Introduction
Review of separation of variables; classification of second order equations; Sturm-Liouville boundary value problems; maximum principles for elliptic & parabolic equations. Green's functions & Neumann problem for Laplace & heat equations. Cauchy problem for heat & wave equations; weak form solutions in the context of the finite element method.

Learning Objectives
After successfully completing this course you should be able to:
• Solve simple first order PDE's and classify second order PDEs
• Use the method of characteristics for the wave equation
• Use the method of seperation of variables in a variety of situations for the heat, wave and Laplace equations
• Understand the importance and role of the maximum and uniqueness principles of elliptic and parabolic equations
• Understand self-adjoint boundary value problems and the Fredholm alternative
• Understand and derive Green's functions
• Present clear and consise mathematical arguments in assignments and exams

Class Contact
3 Lecture hours, 1 Tutorial hour

Assessment Summary
Assignments (1-3): 9%
Mid Semester Exam: 23%
Assignment 4: 3%
Video Assessment: 7%
Assignment 5: 3%
Final Exam: 55%

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.