**
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
T_{E}X
by
T_{T}H,
version 2.70.

On 17 Oct 2004, 21:08.