School of Mathematics and Statistics (SoMaS)

MAS325 Mathematical Methods

This course introduces methods which are useful in many areas of mathematics. The emphasis will mainly be on obtaining approximate solutions to problems which involve a small parameter and cannot easily be solved exactly. These problems will include the evaluation of integrals. Examples of possible applications are: oscillating motions with small nonlinear damping, the effect of other planets on the Earth's orbit around the Sun, boundary layers in fluid flows, electrical capacitance of long thin bodies, central limit theorem correction terms for finite sample size.

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)
No other modules have this module as a prerequisite.

Outline syllabus

• Integral methods and differential equations: Dirac δ-function, Fourier and Laplace transforms, applications to differential equations, Green functions.
• Asymptotic expansions: algebraic equations with small parameter, asymptotic expansion of functions defined by integrals.

Office hours

Aims

• To develop methods for solving differential equations using integral transforms and representations.
• To introduce asymptotic methods for solving algebraic equations.
• To introduce asymptotic methods for evaluating integrals.

Learning outcomes

Teaching methods

Lectures

Assessment

One formal 2 hour written examination. Format: 4 questions from 5.

Reading list