MATLAB Programming for Numerical Analysis. César Pérez López

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1 MATLAB Programming for Numerical Analysis César Pérez López

2 MATLAB Programming for Numerical Analysis Copyright 2014 by César Pérez López This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. ISBN-13 (pbk): ISBN-13 (electronic): Trademarked names, logos, and images may appear in this book. Rather than use a trademark symbol with every occurrence of a trademarked name, logo, or image we use the names, logos, and images only in an editorial fashion and to the benefit of the trademark owner, with no intention of infringement of the trademark. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Publisher: Heinz Weinheimer Lead Editor: Dominic Shakeshaft Editorial Board: Steve Anglin, Mark Beckner, Ewan Buckingham, Gary Cornell, Louise Corrigan, Jim DeWolf, Jonathan Gennick, Jonathan Hassell, Robert Hutchinson, Michelle Lowman, James Markham, Matthew Moodie, Jeff Olson, Jeffrey Pepper, Douglas Pundick, Ben Renow-Clarke, Dominic Shakeshaft, Gwenan Spearing, Matt Wade, Steve Weiss Coordinating Editor: Jill Balzano Copy Editor: Barnaby Sheppard Compositor: SPi Global Indexer: SPi Global Artist: SPi Global Cover Designer: Anna Ishchenko Distributed to the book trade worldwide by Springer Science+Business Media New York, 233 Spring Street, 6th Floor, New York, NY Phone SPRINGER, fax (201) , orders-ny@springer-sbm.com, or visit Apress Media, LLC is a California LLC and the sole member (owner) is Springer Science + Business Media Finance Inc (SSBM Finance Inc). SSBM Finance Inc is a Delaware corporation.f For information on translations, please rights@apress.com, or visit Apress and friends of ED books may be purchased in bulk for academic, corporate, or promotional use. ebook versions and licenses are also available for most titles. For more information, reference our Special Bulk Sales ebook Licensing web page at Any source code or other supplementary material referenced by the author in this text is available to readers at For detailed information about how to locate your book s source code, go to

3 Contents at a Glance About the Author...ix Chapter 1: The MATLAB Environment...1 Chapter 2: MATLAB Language: Variables, Numbers, Operators and Functions...29 Chapter 3: Matlab Language: Development Environment Features...83 Chapter 4: MATLAB Language: M-Files, Scripts, Flow Control and Numerical Analysis Functions Chapter 5: Numerical Algorithms: Equations, Derivatives and Integrals iii

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5 Contents About the Author...ix Chapter 1: The MATLAB Environment...1 Starting MATLAB on Windows. The MATLAB working environment...1 The MATLAB Command Window... 2 Escape and exit to DOS environment commands... 9 Preferences for the Command Window The Command History window The Launch Pad window The Current Directory window The help browser The Workspace window The Editor and Debugger for M-files...24 Help in MATLAB...27 Chapter 2: MATLAB Language: Variables, Numbers, Operators and Functions...29 Variables...29 Vector variables Matrix variables Character variables Numbers...41 Integers Functions of integers and divisibility Alternative bases Real numbers v

6 Contents Functions with real arguments Complex numbers Functions with complex arguments Elementary functions that support complex vector arguments Elementary functions that support complex matrix arguments Random numbers Operators...62 Arithmetic operators Relational operators Logical operators Logical functions Chapter 3: Matlab Language: Development Environment Features...83 General Purpose Commands...83 Commands that Handle Variables in the Workspace Commands that Work with Files in the Operational Environment Commands that Handle Functions Commands that Control the Command Window Start and Exit Commands File Input/Output Commands...97 Opening and Closing Files Reading and Writing Binary Files Reading and Writing Formatted ASCII Text Files Control Over the File Position Exporting and Importing Data to Lotus 123 and Delimited ASCII String and Graphic Formats Sound Processing Functions Chapter 4: MATLAB Language: M-Files, Scripts, Flow Control and Numerical Analysis Functions MATLAB and Programming The Text Editor Scripts vi

7 Contents Functions and M-files. Eval and Feval Local and Global Variables Data Types Ordinary Differential Equations with Boundary Conditions Chapter 5: Numerical Algorithms: Equations, Derivatives and Integrals Solving Non-Linear Equations The Fixed Point Method for Solving x = g (x) Newton s Method for Solving the Equation f (x) = Schröder s Method for Solving the Equation f (x) = Systems of Non-Linear Equations The Seidel Method The Newton Raphson Method Interpolation Methods Lagrange Polynomial Interpolation Newton Polynomial Interpolation Numerical Derivation Methods Numerical Derivation via Limits Richardson s Extrapolation Method Derivation Using Interpolation (n + 1 nodes) Numerical Integration Methods The Trapezium Method Simpson s Method Ordinary Differential Equations Euler s Method Heun s Method The Taylor Series Method vii

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9 About the Author César Pérez López is a Professor at the Department of Statistics and Operations Research at the University of Madrid. César is also a Mathematician and Economist at the National Statistics Institute (INE) in Madrid, a body which belongs to the Superior Systems and Information Technology Department of the Spanish Government. César also currently works at the Institute for Fiscal Studies in Madrid. ix

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11 Coming Soon MATLAB Differential Equations, MATLAB Control Systems Engineering, MATLAB Linear Algebra, MATLAB Differential and Integral Calculus, MATLAB Matrix Algebra, xi