School of Mathematics School of Mathematics
Course 3E1 2003-04 (JS Engineering, option JS MSISS )
Lecturer: Dr John Stalker
Requirements/prerequisites: 2E1 and 2E2 (Calculus and elementary ODE. Laplace transforms. Theory of series.)

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

The main topics are stable, but the list of subtopics is subject to change, particularly those towards the end of the course.

#### 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

File translated from TEX by TTH, version 2.70.
On 17 Oct 2004, 21:08.