MAS325 Mathematical Methods

Semester 2, 2017/18 10 Credits
Lecturer: Dr Nils Mole uses MOLE Reading List
Aims Outcomes Teaching Methods Assessment

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.
  • Differential equations with a small parameter.



Aims

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

Learning outcomes

    Teaching methods

    Lectures


    20 lectures, no tutorials

    Assessment

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

    Reading list

    Type Author(s) Title Library Blackwells Amazon
    C Barndorff-Nielsen and Cox Asymptotic Techniques For Use In Statistics 519.5 (B) Blackwells Amazon
    C Bender and Orszag Advanced Mathematical Methods For Scientists And Engineers I: Asymptotic Methods and Perturbation Theory 515.350245 (B) Blackwells Amazon
    C Copson Asymptotic Expansions 3 PER 510.5/CAM Blackwells Amazon
    C Hinch Perturbation Methods 517.9 (H) Blackwells Amazon
    C Jordan and Smith Mathematical Techniques 510 (J) Blackwells Amazon
    C Kevorkian and Cole Multiple Scale And Singular Perturbation Methods 517.9 (K) Blackwells Amazon
    C King, Billingham and Otto Differential Equations 515.35 (K) Blackwells Amazon
    C Lin and Segel Mathematics Applied To Deterministic Problems In The Natural Sciences 510 (L) Blackwells Amazon
    C Olver Asymptotics And Special Functions 517.5217 (O) Blackwells Amazon
    C Van Dyke Perturbation Methods In Fluid Mechanics 532 (V) Blackwells Amazon

    (A = essential, B = recommended, C = background.)

    Most books on reading lists should also be available from the Blackwells shop at Jessop West.