units

MTH3011

Faculty of Science

18 September 2017 18 November 2024
Monash University

Undergraduate - Unit

This unit entry is for students who completed this unit in 2013 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

print version

6 points, SCA Band 2, 0.125 EFTSL

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LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
OfferedClayton First semester 2013 (Day)
Coordinator(s)Associate Professor Michael Page

Synopsis

Introduction to PDEs; first-order PDEs and characteristics, the advection equation. Finite-difference methods for ODEs, truncation error. The wave equation: exact solution, reflection of waves. The heat equation: exact solution, fixed and insulating boundary conditions. Forward, backward and Crank-Nicholson numerical methods for the heat equation, truncation errors and stability analysis. Types of second-order PDEs; boundary and/or initial conditions for well-posed problems. Exact solutions of Laplace's equation. Iterative methods for Laplace's equation; convergence. Numerical methods for the advection equation; upwind differencing. Separation of variables for the wave and heat equations.

Outcomes

On completion of this unit students will be able to:

  1. Understand the role of partial differential equations in the mathematical modelling of physical processes;

  1. Solve a range of first-order partial differential equations including using the 'method of characteristics';

  1. Appreciate the properties of the three basic types of linear second-order partial differential equations, including suitable initial and/or boundary conditions;

  1. Understand the mathematical properties of the diffusion equation, wave equation and Laplace's equation and solve them exactly under some simple conditions;

  1. Analyse and interpret simple applications modelled by the advection equation, diffusion equation and Laplace's equation;

  1. Understand the principles of finite-difference approximation of ordinary and partial differential equations and appreciate the advantages and disadvantages of a range of useful numerical techniques, including their stability;

  1. Evaluate numerical solutions of some partial differential equations using computers, and display those results graphically.

Assessment

Examination (3 hours): 70%
Assignments and tests: 25%
Laboratory work: 5%

Chief examiner(s)

Associate Professor Michael Page

Contact hours

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

Prerequisites

MTH2010 or MTH2015, and MTH2032, or equivalent