(Advances in applied mathematics) Dean G. Duffy - Advanced engineering mathematics with MATLAB-Chapman & Hall_CRC (2016)

Advances in Applied Mathematics FOURTH EDITION Advanced Engineering Mathematics with MATLAB® Dean G Duffy Advances in Applied Mathematics Series Editor: Daniel Zwillinger Published Titles Advanced Engineering Mathematics with MATLAB, Fourth Edition Dean G Duffy CRC Standard Curves and Surfaces with Mathematica®, Third Edition David H von Seggern Dynamical Systems for Biological Modeling: An Introduction Fred Brauer and Christopher Kribs Fast Solvers for Mesh-Based Computations Maciej Paszy´nski Green’s Functions with Applications, Second Edition Dean G Duffy Introduction to Financial Mathematics Kevin J Hastings Linear and Integer Optimization: Theory and Practice, Third Edition Gerard Sierksma and Yori Zwols Markov Processes James R Kirkwood Pocket Book of Integrals and Mathematical Formulas, 5th Edition Ronald J Tallarida Stochastic Partial Differential Equations, Second Edition Pao-Liu Chow FOURTH EDITION Advanced Engineering Mathematics with MATLAB® CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2017 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed on acid-free paper Version Date: 20161121 International Standard Book Number-13: 978-1-4987-3964-1 (Hardback) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging‑in‑Publication Data Names: Katzman, Steve (IT auditor) Title: Operational assessment of IT / Steve Katzman Description: Boca Raton, FL : CRC Press, 2016 | Series: Internal audit and IT audit ; | Includes bibliographical references and index Identifiers: LCCN 2015037136 | ISBN 9781498737685 Subjects: LCSH: Information technology Management | Information technology Auditing | Auditing, Internal Classification: LCC HD30.2 K3857 2016 | DDC 004.068 dc23 LC record available at http://lccn.loc.gov/2015037136 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Dedicated to the Brigade of Midshipmen and the Corps of Cadets v Contents Dedication v Contents vii Acknowledgments xv Author xvii Introduction xix List of Definitions xxiii CLASSIC ENGINEERING MATHEMATICS 1.5 Chapter 1: First-Order Ordinary Differential Equations x 0.5 −0.5 −1 −2 −1.5 −1 −0.5 0.5 1.5 2.5 t 1.1 Classification of Differential Equations 1.2 Separation of Variables 1.3 Homogeneous Equations 16 vii viii Advanced Engineering Mathematics with MATLAB 1.4 Exact Equations 17 1.5 Linear Equations 20 1.6 Graphical Solutions 31 1.7 Numerical Methods 34 Chapter 2: Higher-Order Ordinary Differential Equations v −1 45 −2 −3 −3 −2 −1 x 2.1 Homogeneous Linear Equations with Constant Coefficients 49 2.2 Simple Harmonic Motion 57 2.3 Damped Harmonic Motion 61 2.4 Method of Undetermined Coefficients 66 2.5 Forced Harmonic Motion 71 2.6 Variation of Parameters 78 2.7 Euler-Cauchy Equation 83 2.8 Phase Diagrams 87 2.9 Numerical Methods 91  a11  a21      am1 a12 a22 am2 ··· ··· ···  a1n a2n       amn Chapter 3: Linear Algebra 3.1 Fundamentals of Linear Algebra 97 97 3.2 Determinants 104 3.3 Cramer’s Rule 108 3.4 Row Echelon Form and Gaussian Elimination 111 3.5 Eigenvalues and Eigenvectors 124 3.6 Systems of Linear Differential Equations 133 3.7 Matrix Exponential 139 Table of Contents ix z (0,0,1) n C2 C3 (0,1,0) y Chapter 4: Vector Calculus 145 C1 (1,0,0) x 4.1 Review 145 4.2 Divergence and Curl 152 4.3 Line Integrals 156 4.4 The Potential Function 161 4.5 Surface Integrals 162 4.6 Green’s Lemma 169 4.7 Stokes’ Theorem 173 4.8 Divergence Theorem 179 amplitude spectrum (ft) times 10000 10000.0 1000.0 100.0 Chapter 5: Fourier Series 10.0 1.0 187 0.1 Bay bridge and tunnel 10 100 1000 10000 5.1 Fourier Series 187 5.2 Properties of Fourier Series 198 5.3 Half-Range Expansions 206 5.4 Fourier Series with Phase Angles 211 5.5 Complex Fourier Series 213 5.6 The Use of Fourier Series in the Solution of Ordinary Differential Equations 217 5.7 Finite Fourier Series 225 4.0 3.0 y=tan( πx) Chapter 6: The Sturm-Liouville Problem x y= y 2.0 1.0 0.0 −1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 239 3.5 x 6.1 Eigenvalues and Eigenfunctions 239 ...Advances in Applied Mathematics FOURTH EDITION Advanced Engineering Mathematics with MATLAB® Dean G Duffy Advances in Applied Mathematics Series Editor: Daniel Zwillinger Published Titles Advanced Engineering. .. because of the increasing use of probabilistic concepts in engineering analysis To incorporate this development into an engineering mathematics course we adopt a curriculum that begins with Fourier... STEM (science, technology, engineering, and mathematics) student must master vast quantities of applied mathematics This is why I wrote Advanced Engineering Mathematics with MATLAB Three assumptions