Mathematical Methods 3M1

The lecturers are Andrew Bassom and Nev Fowkes Rm 1.15 (fowkes@maths.uwa.edu.au).

Unit Aims

The primary objective is to introduce the methods, both analytic and numerical, used to solve the ordinary and partial differential equations that arise out of Engineering and Science. The archetype equations of mathematical physics will be discussed, and the expected solution behaviour illustrated by example. No text is prescribed however Boyce and diPrima is a useful reference for much of the material. Students are expected to use Maple or Mathematica.

Assessment

A final exam worth 70% of the final grade. There will be a total of three (take home assignments + tests) each worth 10% of the final grade.
The final exam will be of 3 hours duration and will consist of 6 questions not of equal value covering all the material of the course. Mathematica will not be directly examined. Mathematica output may be supplied for use in the exam. Authorized calculators only will be allowed. The exam will be similar to the 3M1 exam in 2004.

Important Notices

Important notices will be posted here. Such notices include the timing of tests, assignment due dates etc.
The solutions to all assignments are now available.
Please check to see if the marks have been entered correctly for ALL marked assingmentsand the test.

The 2004 Exam in 3M1 is displayed below.
The exam this year will be similar to last years exam. Notes and books will not be allowed in the exam and only the approved calculators will be allowed. Scrutineers will be asked to remove any unapproved calculators. Good luck!
Please read the following document regarding plagiarism.

Course Outline

Ordinary Differential Equations

Summary of exact techniques, including algebraic packages. Series solutions. Singularities. (5) Two point boundary value problems. Sturm-Liouville Theory. (3) Asymptotic Methods. (2) .

Partial Differential Equations

The Archetype Equations (Heat, Wave, Potential, ...) Separation of Variables. Finite and Infinite transforms.(6)
Fourier Series; convergence, singularity extraction.(3)
Spherical and cylindrical geometry problems. (2)
Classification of 2nd Orders (2). Hyperbolics (2).

Approximation Techniques

Regular and singular perturbations (3). Integral evaluations WKBJ technique.

Algebraic Packages

As indicated a knowledge of either Mathematica or Maple is required. For introductory notes see Mathematica and Maple.

Assignments

Miscellaneous Items/Links

Student check mark here

Author: Dr Neville Fowkes
Date last modified Mar 1 2005