Applied numerical methods using MATLAB®

In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online. Cover Page......Page 1 Title Page......Page 2 Copyright 2005 by John Wiley & Sons, Inc.......Page 3 1 MATLAB Usage and Computational Errors......Page 5 3 Interpolation and Curve Fitting......Page 6 6 Ordinary Differential Equations......Page 7 9 Partial Differential Equations......Page 8 Preface......Page 10 1 MATLAB Usage and Computational Errors......Page 12 2 System of Linear Equations......Page 82 3 Interpolation and Curve Fitting......Page 128 4 Nonlinear Equations......Page 190 5 Numerical Differentiation/Integration......Page 220 6 Ordinary Differential Equations......Page 274 7 Optimization......Page 332 8 Matrices and Eigenvalues......Page 382 9 Partial Differential Equations......Page 412 Appendix A. Mean Value Theorem......Page 472 Appendix B. Matrix Operations/Properties......Page 474 Appendix C. Differentiation with Respect to a Vector......Page 482 Appendix D. Laplace Transform......Page 484 Appendix E. Fourier Transform......Page 486 Appendix F. Useful Formulas......Page 488 Appendix G. Symbolic Computation......Page 492 Appendix H. Sparse Matrices......Page 500 Appendix I. MATLAB......Page 502 References......Page 508 Subject Index......Page 510 Index for MATLAB Routines......Page 514 Index for Tables......Page 520 Cover Page 1 Title Page 2 Copyright 2005 by John Wiley & Sons, Inc. 3 CONTENTS 5 1 MATLAB Usage and Computational Errors 5 2 System of Linear Equations 6 3 Interpolation and Curve Fitting 6 4 Nonlinear Equations 7 5 Numerical Differentiation/Integration 7 6 Ordinary Differential Equations 7 7 Optimization 8 8 Matrices and Eigenvalues 8 9 Partial Differential Equations 8 Preface 10 1 MATLAB Usage and Computational Errors 12 2 System of Linear Equations 82 3 Interpolation and Curve Fitting 128 4 Nonlinear Equations 190 5 Numerical Differentiation/Integration 220 6 Ordinary Differential Equations 274 7 Optimization 332 8 Matrices and Eigenvalues 382 9 Partial Differential Equations 412 Appendix A. Mean Value Theorem 472 Appendix B. Matrix Operations/Properties 474 Appendix C. Differentiation with Respect to a Vector 482 Appendix D. Laplace Transform 484 Appendix E. Fourier Transform 486 Appendix F. Useful Formulas 488 Appendix G. Symbolic Computation 492 Appendix H. Sparse Matrices 500 Appendix I. MATLAB 502 References 508 Subject Index 510 Index for MATLAB Routines 514 Index for Tables 520 "Increasingly, scientists and engineers favor MATLAB over conventional programming languages, such as FORTRAN and C when they wish to solve complex problems. This book will enable readers to solve problems without needing to understand all the details of the underlying theory of numerical methods. By providing many examples of the uses of similar functions, it guides them towards the selection of the appropriate MATLAB functions for solving their problem efficiently."--BOOK JACKET