Duration: 22 weeks

Number of lectures per week: 2 lectures plus 1 tutorial

Assessment: Weekly tutorial problems.

End-of-year Examination: One 3-hour examination

Description: This course follows on directly from 2E1/2E2 and develops the mathematics of engineering and physics. It covers Fourier series, Fourier transforms, partial differential equations, linear programming and optimisation, complex analysis.

• Review of Fourier Methods
  • Algebraic Preliminaries
  • Sampling, Aliasing, etc.
  • Definition of Fourier Series, Transform, etc.
  • Fast Fourier Transform
  • Gibbs Phenomenon
  • Regularity and Decay
  • Filtering and Other Applications

• Partial Differential Equations
  • Laplace's Equation
  • The Heat Equation
  • The Wave Equation
  • Some Other Equation(s)
  • Fundamental Solutions
  • Separation of Variables
  • Finite Differences/Finite Elements

• Optimization
  • Linear Programming
  • Kuhn-Tucker
  • Duality
  • Graph Theory

• Complex Analysis
  • Power Series
  • The Cauchy-Riemann Equations
  • Familiar Functions Extended to Complex Domain
  • Complex Integrals
  • Residue Tricks

Textbook:

There is no formal textbook for the course. You can find dozens of books with mytitles like `Advanced Engineering Mathematics' or `Mathematical Methods for Scientists and Engineers' which cover most of the material for the course. In the library you should be able to find one which has a style of presentation you like and which covers most of the topics listed below. When I cover topics which are harder to find I will suggest references.

Oct 17, 2004