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MA40044: Mathematical methods 1

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment: CW 20%, EX 80%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20216 AND take MA20219 AND take MA20220 AND take MA20223
In taking this module you cannot take MA30044
Further information on descriptions Description: Aims & Learning Objectives:
Aims:
To furnish the student with a range of analytic techniques for the solution of ODEs and PDEs with applications to advanced physical problems.
Objectives: Students should be able to obtain the solution of certain ODEs and PDEs, and in cases interpret these in physical terms. They should also be aware of certain analytic properties associated with the solution e.g. uniqueness.

Content:
Sturm-Liouville theory: Reality of eigenvalues. Orthogonality of eigenfunctions. Expansion in eigenfunctions. Approximation in mean square. Statement of completeness. Fourier Transform: As a limit of Fourier series. Properties and applications to solution of differential equations. Frequency response of linear systems. Characteristic functions. Linear and quasi-linear first-order PDEs in two and three independent variables: Characteristics. Integral surfaces. Uniqueness (without proof). Linear and quasi-linear second-order PDEs in two independent variables: Cauchy-Kovalevskaya theorem (without proof). Characteristic data. Lack of continuous dependence on initial data for Caucy problem. Classification as elliptic, parabolic, and hyperbolic. Different standard forms. Constant and nonconstant coefficients. One-dimensional wave equation: d'Alembert's solution. Uniqueness theorem for corresponding Cauchy problem (with data on a spacelike curve). Applications to physical problems. Translate advanced physical problems into mathematical form; obtain and interpret mathematical solutions.
Further information on programme availabilityProgramme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020

MA40044 is Compulsory on the following programmes:

Department of Physics
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)

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