MAS325 Mathematical Methods
|Semester 2, 2021/22||10 Credits|
|Lecturer:||Dr Nils Mole||Timetable||Reading List|
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.
- 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.
- 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 outcomesBy the end of the unit students should be able to demonstrate an understanding of methods for solving differential equations using integral transforms and representations, and an awareness of asymptotic methods for solving algebraic equations and for evaluating integrals.
20 lectures, no tutorials
One formal 2 hour written examination. Format: 4 questions from 5.
|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||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.