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Module Code: EEE1018 Module Title: MATHEMATICS
 Module Provider: Electronic Engineering Short Name: EEE1.MAT Level: HE1 Module Co-ordinator: GOURLEY SA Dr (Maths) Number of credits: 20 Number of ECTS credits: 10
Module Availability
Autumn and Spring Semesters
Assessment Pattern

Unit(s) of Assessment

###### Weighting Towards Module Mark( %)

Coursework Autumn & Spring (exercise sheets and tests)

55%

Examination (Spring)

45%

Module Overview
Prerequisites/Co-requisites
Normal entry requirements for degree course in Engineering
Module Aims
This module is intended to provide students with some of the basic understanding and skills in mathematics needed to follow a degree programme in engineering.

Students with weaker backgrounds in mathematics will be taught separately in the Autumn Semester. All students will be taught together in the Spring Semester.

Learning Outcomes

Students should

·         understand the concepts, terminology and information introduced in the module.

·         demonstrate knowledge of the available methods and be able to select the appropriate technique for a given problem, with an awareness of its possible limitations.

present solutions in a clear and structured way, with accuracy and logical consistency.

Module Content

AUTUMN SEMESTER:

Basic algebra (factorisation, partial fractions, roots of quadratics and other simple equations, linear simultaneous equations), geometry, trigonometry. Trigonometric identities and solutions of trigonometric equations.

Exponential and logarithmic functions and their properties. Odd, even and periodic functions. Concept of a function and inverse functions, trigonometric and inverse trigonometric functions, hyperbolic functions and their inverses, solution of trigonometric and hyperbolic equations.

Complex numbers: real and imaginary parts, polar and exponential form, Argand diagram, exp(jx)=cosx+jsinx, relationship between trigonometric and hyperbolic functions, De Moivre’s theorem and applications.

Concept of derivative and rules of differentiation for a function of one variable. Differentiation of  trigonometric, exponential and logarithmic functions. Applications to gradients, tangents and normals, extreme points and curve sketching. Functions of several variables. The idea that the graph of z=f(x,y) is a surface. First and second order partial derivatives and their meanings as slopes in particular directions. The total differential and applications to errors and rates of change.

Arithmetic and geometric sequences and series.

Various techniques for the evaluation of limits.

Concept of indefinite integration as the inverse of differentiation and standard methods for integration such as substitution, integration by parts and integration of rational functions. Definite integration, areas under curves, use of recurrence relationships, numerical integration. Mean and rms values.

SPRING SEMESTER:

Fourier Series

Calculation of the Fourier Series of a periodic function. Representation of a Fourier Series in complex form.

Further integration

Hyperbolic function - definitions, identities and integrals. Conic sections - equations in implicit and parametric form. Integral requiring trigonometric or hyperbolic substitutions. Calculation of areas under curves given implicitly. Calculation of the length of a curve (given explicitly or as parametric equations)

Multiple Integration

Evaluation of multiple integrals with both constant and non-constant limits. Interpretation of the region of integration of a multiple integral and evaluation of multiple integrals by changing the order of integration and use of polar co-ordinates.

Power series, limits and approximations

Binomial expansion. Power series including Maclaurin and Taylor series expansions. The Newton-Raphson method. Calculation of approximations and limits using power series. Calculation of limits using L'Hôpital's Rule.

Ordinary Differential Equations

Classification of differential equations. First order differential equations with variables separable, and the use of an integrating factor. First and second order linear differential equations with constant coefficients (homogeneous and non-homogeneous where the RHS is an exponential, trigonometric or polynomial function).

Methods of Teaching/Learning
Lectures and examples classes. In the Autumn semester students are split into two classes according to mathematical ability and/or prior knowledge of mathematics. In the Spring semester students are all taught together.
Selected Texts/Journals
Engineering Mathematics, K.A. Stroud, 5th edition or later, Palgrave Macmillan
Engineering Mathematics, A Croft, R Davison, M Hargreaves; Prentice-Hall (2001)

Modern Engineering Mathematics, James G, 3rd ed, Prentice-Hall, 2001 (ISBN 01301 83199)

Last Updated

12 August 2010

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