# MTH3011 - Partial differential equations

## 6 points, SCA Band 2, 0.125 EFTSL

#### Offered

Clayton First semester 2007 (Day)

#### Synopsis

Classification of second-order linear PDEs; appropriate boundary and/or initial conditions and well-posed problems; parabolic equations: the diffusion equation, the maximum principle, explicit and implicit finite-difference techniques, numerical instability; hyperbolic equations: the wave equation; the advection equation, the method of characteristics, numerical techniques, the CFL condition, elliptic equations: Laplace's equation, iterative numerical techniques.

#### Objectives

On completion of this unit, students will understand the role of PDEs in the mathematical modelling of physical processes; be able to distinguish between the three basic types of PDEs and recognise appropriate initial and/or boundary conditions; be able to solve simple problems which are modelled by the wave equation, diffusion equation and Laplace's equation and understand their mathematical properties; understand the principles of finite-difference approximation; appreciate the advantages and disadvantages of a range of numerical techniques; be able to identify when a technique is susceptible to numerical instability; understand some basic iterative methods; have practical experience in determining an approximate numerical solution of PDEs using computers, including for the graphical display of the results.

#### Assessment

Examination (3 hours): 60%

Assignments and tests: 30%

Laboratory work: 10%

#### Contact hours

Three 1-hour lectures and one 2-hour laboratory class per week

#### Prerequisites

MTH2010 and MTH2032 or equivalent

#### Prohibitions

MAT3022, ASP3111, ATM3141