10098 (v.2) Mathematical Methods 301

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Area:	Department of Mathematics and Statistics
Credits:	25.0
Contact Hours:	4.0
Lecture:	3 x 1 Hours Weekly
Laboratory:	1 x 1 Hours Weekly
Prerequisite(s):	8127 (v.5) Mathematics 201 or any previous version
Syllabus:	Separation of variables for partial differential equations (including Laplace's equation and the diffusion equation). Scaling methods and dimensional analysis. Laplace transforms. Sturm-Liouville systems and orthogonal function expansions. Special functions including Bessel and modified Bessel functions, Legendre polynomials. Generalised functions. Green's function method. Functions of a complex variable. Cauchy's theorem. Taylor and Laurent series. Residue calculus. Inverse Laplace transforms.
Unit Outcomes:	On completion of this unit, students will be able to solve some partial differential equations using the method of separation ofvariables. Approximate a function using a generalized Fourier series. Understand the use of Green's function for solving a Sturm-Liouville system. Understand the properties of elementary functions of a complex variable. Use complex integration to evaluate integrals.
Text and references listed above are for your information only and current as of September 30, 2003. Please check with the unit coordinator for up-to-date information.
Unit References:	Andrews, L.C. 1986 Elementary partial differential equations with boundary value problems. Acad. Press. Boyce, W.E. and DiPrima, R.C. any edition. Elementary differential equations and boundary value problems. Wiley. Fisher, S.D. 1986 Complex Variables, 2nd ed. Wadsworth & Brooks-Cole. Johnson, D.E. and Johnson, J.R. 1982. Mathematical methods. Prentice- Hall. Trim, E.W. 1990. Applied partial differential equations, PWS-Kent
Unit Texts:	no text required
Unit Assessment Breakdown:	Assignment 1 15%, Assignment 2 15%, Web quiz 5%, End of Semester Examination 65%
Year Location Period Internal Area External Central External 2004 Bentley Campus Semester 1 Y