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MA30362: Methods for differential equations

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 12 [equivalent to 24 CATS credits]
Notional Study Hours: 240
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EXCB 100%
Assessment Detail:
  • MA32062 Closed-book written examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA22021 OR ( take MA20223 AND take MA20221 )
In taking this module you cannot take MA30044
Learning Outcomes: By the end of the unit, you should be able to: (i) find explicit solutions to differential equations using Sturm-Liouville problems and the Fourier transform, (ii) find approximate solutions to differential equation using asymptotic methods, and (iii) find and solve the differential equations satisfied by functions minimising integrals.


Synopsis: Many physical processes can be modelled by ordinary and partial differential equations, and an important task in applied mathematics is then to solve these equations. In this unit you will encounter various methods for doing this, building on the methods you learnt in applied units in Year 2.

Content: Sturm-Liouville problems, orthogonal polynomials, Fredholm alternative, Fourier transform (convolution theorem, inversion formula, delta function as Fourier transform of 1, solving ODEs and PDEs). Calculus of variations in 1-d: Euler-Lagrange equations and solution in different cases. Asymptotics: polynomial equations, asymptotic series, method of stationary phase, WKB, method of strained coordinates, method of multiple scales, boundary layers.

Course availability:

MA30362 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
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