Ma271 Mathematics For Electonic & Electrical Engineering.
(Rakesh)
Basic Information School Fac Engineering Known as MA271. Session and Semester Semester One, 2002  2003 Credit 10 Credit Points Unit Leader Study Assessment 20% coursework, 80% closed book examination (formula sheet provided) Coursework 3 pieces, worth 20/3% each. Deadlines will be available at the start of the unit Teaching Referral On referral, this unit will be assessed 100% by examination. Syllabus Approved Description Aims To give students a solid grounding in mathematical methods and ideas that they will use later in their degree course. Objectives To give students an understanding of Laplace transform theory, elementary Fourier series, Eigenvalues and eigenvectors, complex variable theory and vector calculus. Learning Outcomes General Transferable (key) Skills Having successfully completed the module, you will be able to: understand and use mathematical techniques as and when they arise later in your degree course. Topics Covered Laplace Transform Theory The (onesided) 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 sawtooth 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 nonconstant 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 simpleharmonic 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. The point at infinity. (About 4 lectures) Vector Calculus A survey of div, grad and curl and associated theorems  geometric interpretation. Stokes' theorem. The Laplacian in polar coordinates. (About 10 lectures) Resources Background Resources 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. Taught to MA271 Pt II BEng Computer Engineering (Compulsory) Pt II MEng Computer Engineering (Compulsory) Pt II BEng Electrical Engineering (Compulsory) Pt II MEng Electrical Engineering (Compulsory) Pt II MEng Electrical Engineering with European Studies (Compulsory) Pt II MEng Engineering Management, Electrical Engineering (Compulsory) Pt II BEng Electronic Engineering (Compulsory) Pt II MEng Electronic Engineering (Compulsory) Pt II MEng Electronic Engineering and Tripartite Diploma (Compulsory) Pt Eng Electronic Engineering with European Studies (Compulsory) Pt II Eng Engineering Management, Electronic Engineering (Compulsory) Pt II BEng Electromechanical Engineering (Compulsory) Pt II MEng Electromechanical Engineering (Compulsory) Pt II MEng Electromechanical Engineering with European Studies (Compulsory) Pt II MEng Engineering Management, Electromechanical Engineering (Compulsory) Pt II MEng Electronics (Compulsory) Pt II MEng Electronics with Artificial Intelligence (Compulsory) Pt II MEng Electronics with Computer Systems (Compulsory) Pt II MEng Electronics with Microelectronics (Compulsory) Pt II MEng Electronics with Optical Communications (Compulsory) Pt II MEng Electronics with Telecommunications (Compulsory
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