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SOLVING APPLIED MATHEMATICAL PROBLEMS WITH MATLABC8250_FM.indd 1 9/19/08 4:21:15 PMThis page intentionally left blank SOLVING APPLIED MATHEMATICAL PROBLEMS WITH MATLABDingy XueYangQuan ChenC8250_FM.indd 3 9/19/08 4:21:15 PMChapman & Hall/CRCTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2009 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-13: 978-1-4200-8250-0 (Hardcover)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 can-not 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.copy-right.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 pro-vides 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 DataXue, Dingyu.Solving applied mathematical problems with MATLAB / Dingyu Xue, YangQuan Chen.p. cm.Includes bibliographical references and index.ISBN-13: 978-1-4200-8250-0ISBN-10: 1-4200-8250-71. Engineering mathematics--Data processing. 2. MATLAB. 3. Numerical analysis--Data processing. 4. Mathematical optimization--Data processing. I. Chen, YangQuan, 1966- II. Title. TA331.X84 2009510.2855133--dc22 2008025953Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.comC8250_FM.indd 4 9/19/08 4:21:15 PMContentsPreface xi1 Computer Mathematics Languages An Overview 11.1 Computer Solutions to Mathematics Problems . . . . . . . . 11.1.1 Why should we study computer mathematics language? 11.1.2 Analytical solutions versus numerical solutions . . . . . 41.1.3 Mathematics software packages: an overview . . . . . . 51.2 Summary of Computer Mathematics Languages . . . . . . . . 61.2.1 A brief historic review of MATLAB . . . . . . . . . . . 61.2.2 Three widely used computer mathematics languages . 71.2.3 Introduction to free scientic open-source softwares . . 71.3 Outline of the Book . . . . . . . . . . . . . . . . . . . . . . . 8Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Fundamentals of MATLAB Programming 112.1 Fundamentals of MATLAB Programming . . . . . . . . . . . 122.1.1 Variables and constants in MATLAB . . . . . . . . . . 122.1.2 Data structure . . . . . . . . . . . . . . . . . . . . . . . 132.1.3 Basic structure of MATLAB . . . . . . . . . . . . . . . 142.1.4 Colon expressions and sub-matrices extraction . . . . . 152.2 Fundamental Mathematical Calculations . . . . . . . . . . . . 162.2.1 Algebraic operations of matrices . . . . . . . . . . . . . 162.2.2 Logic operations of matrices . . . . . . . . . . . . . . . 182.2.3 Relationship operations of matrices . . . . . . . . . . . 192.2.4 Simplications and presentations of analytical results . 192.2.5 Basic number theory computations . . . . . . . . . . . 212.3 Flow Control Structures of MATLAB Language . . . . . . . 222.3.1 Loop control structures . . . . . . . . . . . . . . . . . . 222.3.2 Conditional control structures . . . . . . . . . . . . . . 242.3.3 Switch structure . . . . . . . . . . . . . . . . . . . . . . 252.3.4 Trial structure . . . . . . . . . . . . . . . . . . . . . . . 262.4 Writing and Debugging MATLAB Functions . . . . . . . . . 272.4.1 Basic structure of MATLAB functions . . . . . . . . . 272.4.2 Programming of functions with variable inputs/outputs 302.4.3 Inline functions and anonymous functions . . . . . . . 312.5 Two-Dimensional Graphics . . . . . . . . . . . . . . . . . . . 312.5.1 Basic statements of two-dimensional plotting . . . . . . 322.5.2 Other two-dimensional plotting statements . . . . . . . 342.5.3 Implicit function plotting and applications . . . . . . . 36vvi Solving Applied Mathematical Problems with MATLAB2.5.4 Graphics decorations . . . . . . . . . . . . . . . . . . . 362.6 Three-Dimensional Graphics . . . . . . . . . . . . . . . . . . 392.6.1 Plotting of three-dimensional curves . . . . . . . . . . . 392.6.2 Plotting of three-dimensional surfaces . . . . . . . . . . 402.6.3 Viewpoint setting in 3D graphs . . . . . . . . . . . . . 43Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Calculus Problems 473.1 Analytical Solutions to Calculus Problems . . . . . . . . . . . 473.1.1 Analytical solutions to limit problems . . . . . . . . . . 483.1.2 Analytical solutions to derivative problems . . . . . . . 503.1.3 Analytical solutions to integral problems . . . . . . . . 553.2 Series Expansions and Series Evaluations . . . . . . . . . . . 583.2.1 Taylor series expansion . . . . . . . . . . . . . . . . . . 593.2.2 Fourier series expansion . . . . . . . . . . . . . . . . . 623.2.3 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.2.4 Sequence product . . . . . . . . . . . . . . . . . . . . . 673.3 Numerical Dierentiation . . . . . . . . . . . . . . . . . . . . 673.3.1 Numerical dierentiation algorithms . . . . . . . . . . 683.3.2 Central-point dierence algorithm . . . . . . . . . . . . 693.3.3 Gradient computations of functions with two variables 713.4 Numerical Integration Problems . . . . . . . . . . . . . . . . 723.4.1 Numerical integration from given data using trapezoidalmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.4.2 Numerical integration of single variable functions . . . 743.4.3 Numerical solutions to double integrals . . . . . . . . . 773.4.4 Numerical solutions to triple integrals . . . . . . . . . . 793.5 Path Integrals and Line Integrals . . . . . . . . . . . . . . . . 803.5.1 Path integrals . . . . . . . . . . . . . . . . . . . . . . . 803.5.2 Line integrals . . . . . . . . . . . . . . . . . . . . . . . 813.6 Surface Integrals . . . . . . . . . . . . . . . . . . . . . . . . . 833.6.1 Scalar surface integrals . . . . . . . . . . . . . . . . . . 833.6.2 Vector surface integrals . . . . . . . . . . . . . . . . . . 84Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854 Linear Algebra Problems 894.1 Inputting Special Matrices . . . . . . . . . . . . . . . . . . . 904.1.1 Numerical matrix input . . . . . . . . . . . . . . . . . . 904.1.2 Dening symbolic matrices