Advanced Differential Equations

Description

This course introduces students to the modern theory and methods of ordinary and partial differential equations. It builds on the classical foundations of differential equations studied in second year. Ordinary and partial differential equations form an essential part of the mathematical background required for engineering and the physical sciences. A large number of real-life problems can be modelled using differential equations, making the subject one of the most widely applicable areas of mathematics. The course concentrates on some fundamental analytical and numerical methods for applied differential equations arising from the mathematical modelling of physical, chemical and biological systems.

Availability

Callaghan Campus

  • Semester 2 - 2015

Learning Outcomes

1. Have a broad overview of ordinary and partial differential equations as well as an appreciation of the application of analysis and linear algebra in studying differential equations.

2. Have the skills to build mathematical models of relevant real-world problems based on differential equations.

3. Be able to solve these differential equations using appropriate computer software if necessary, and to interpret the solutions.

4. Understand the concepts of accuracy, consistency, stability and convergence of numerical schemes for solving differential equations.

Content

(1) Ordinary Differential Equations

  • (a) Existence and uniqueness theory for ordinary differential equations
  • (b) Stability theory for linear and nonlinear ordinary differential equations
  • (c) Stability and convergence of numerical techniques, and numerical schemes for stiff ordinary differential equations


(2) Partial Differential Equations

  • (a) Modelling with partial differential equations
  • (b) Classical solution techniques and weak solutions
  • (c) Numerical methods for partial differential equations

Assumed Knowledge

MATH2800 and MATH2320 or MATH2470 and MATH2320

Assessment Items

Quiz: Quiz (x2)

Written Assignment: Assignments (x3)

Formal Examination: End of Semester Exam

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

Tutorial and computer lab work will be integrated with lecture material as required.