Electronics and Computer Science (ECS), University of Southampton

To give students a solid grounding in mathematical methods and ideas that they will use later in their degree course.

Module Details

Title: Mathematics 2
Code: MATH2021

Credits: 7.5
Semester: 1

Programmes in which this module is compulsory

• BEng Electromechanical Engineering (HH36)
• MEng Electromechanical Engineering (HHH6)
• MEng Electonic Eng with MSS (H691)
• MEng Electronic Eng wPower Sys (H690)
• MEng Electrical Engineering (H601)
• Electronic Engineering (H603)
• BEng Electrical Engineering (H620)
• BEng Electronic Engineering (H610)

• Mathematical methods of Laplace transform theory, elementary Fourier series, eigenvalues and eigenfunctions, complex variable theory and vector calculus.

• Laplace Transform Theory
  • The (one-sided) Laplace transform and its existence. Use of Laplace transforms in solving simple ODEs with constant coefficients and given boundary conditions. Step functions and their transforms. Laplace transforms of standard functions. Uniqueness of the inverse. Elementary properties - linearity, first and second shifting theorems, change of scale. Transforms of derivatives and integrals and of products with powers of t. Transforms of periodic functions.The limit of F(s) as s->infinity. The initial and final value theorems and their uses. Laplace transforms of some further special functions - the saw-tooth function, the dirac delta function. Theorems relating to inversion. The solution of slightly more complicated ordinary differential equations with given initial or boundary conditions - constant coefficient equations, simultaneous equations, some equations with non-constant coefficients, equations with discontinuous forcing terms. (About 8 lectures)
• Fourier series:
  • Definition of Fourier series. Calculation of coefficients in easy cases. Examples of whole and half range series over various ranges. Elementary properties. (About 5 lectures)
• Eigenvalues, eigenvectors and eigenfunctions:
  • Eigenvalues and eigenvectors of matrices. Simple harmonic equation. Eigenvalues and eigenfunctions of the simple-harmonic equation with various boundary conditions. Applications of eigenvalues, eigenvectors and eigenfunctions. (About 5 lectures)
• Complex Variable Theory
  • Revision of complex numbers including the polar form, de Moivre's theorem, simple complex functions, loci in the argand diagram, differentiability and the Cauchy-Riemann equations. (About 4 lectures)
• Vector Calculus
  • A survey of div, grad and curl and associated theorems - geometric interpretation.Divergence theorem and Stokes' theorem. The Laplacian in polar co-ordinates. (About 10 lectures)

• Lecture, 1 hour, Three times per week
• Tutorial, 1 hour, Once per week

• 80% - 2 hour written examination using Formula sheet, frequency: 1
• 20% - Coursework assignaments, frequency: 3

Referral policy: On referral, this unit will be assessed by examination.

Background textbook:

Stephenson and Radmore Advanced Mathematical Methods for Engineering and Science Students Cambridge

Jeffrey Mathematics for Engineers and Scientists Nelson, 2nd Edition

Greenberg MD, Advanced Engineering Mathematics, Prentice Hall 1999.

Kreyszig E, Advanced Engineering Mathematics Wiley, 1979

Spiegel M R, Schaum's Outline of Theory and Problems of Vector Analysis Schaum

Spiegel M R, Schaum's Outline of Theory and Problems of Laplace Transforms Schaum

Many other examples (including old examination questions and solutions) are available via the web. Students are also recommended to attend the Mathematics Workshop.