Engineering Mathematicsnotes

Engineering Mathematicsnotes - Department of Mathematical...

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Department of Mathematical Sciences Engineering Mathematics 1 EG1006 Ian Craw, Stuart Dagger and John Pulham
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ii September 26, 2001, Version 2.0 Copyright 2001 by Ian Craw, Stuart Dagger, John Pulham and the University of Aber- deen All rights reserved. Additional copies may be obtained from: Department of Mathematical Sciences University of Aberdeen Aberdeen AB9 2TY DSN: mth200-101980-3
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Foreword What the Course Tries to Do It is always a good idea to start by saying what we are trying to do, and how you will recognise if you have succeeded! Modern education jargon sums up this by emphasising “aims” and “learning outcomes. Here they are in the same form as in the “Catalogue of Courses”. It is hard to understand what the objectives mean before you have finished the course; but at that stage, you should come back here and check that they do make sense. If they don’t, you may have missed something important. Aims The overall aim of the mathematics part of the course is to continue the introduction of elementary mathematical ideas useful in the study of Engineering, laying particular emphasis on algebraic structure and methods. Learning Outcomes By the end of the course the student should: be familiar with the concept of a complex number and be able perform algebraic operations on complex numbers, both with numeric and symbolic entries; give a geometrical interpretation of a complex number in terms of the Argand diagram; be able to state and use de Moivre’s theorem; solve simple equations with complex roots, and in particular describe geometrically the roots of unity; define the discrete Fourier transform in terms of complex numbers and give a brief description potential applications; and be aware of the fundamental theorem of algebra, be able to prove that complex roots of a real polynomial occur in pairs, and use these results and the remainder theorem to perform simple polynomial factorisation. be familiar with the concept of a matrix and be able to perform algebraic operations on matrices, both with numeric and symbolic entries; iii
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iv be able to define a determinant and calculate one both directly and by using row and column operations; understand the definition and use of the inverse of a non-singular matrix, and be aware of the adjugate formula; be able to express linear systems of equations in terms of matrices, solve simple systems both using inverses and reduction to triangular form, and be able to describe the nature of the solutions geometrically; be able to compute inverses using Gaussian reduction and explain the method in terms of elementary matrices; These Notes The course is presented in two parts; a “calculus” side, given by Prof Hall and an “algebra” side, given by me. This is a very rough division; some material on calculus, specifically Chapter 5 will be given in this part of the course. Think of the division more as making your experience of lectures more varied, rather than one based on subject. These notes are
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This note was uploaded on 09/09/2011 for the course ECON 323 taught by Professor Prof. during the Spring '11 term at UAA.

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Engineering Mathematicsnotes - Department of Mathematical...

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