Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted.
New to the Third Edition
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A chapter on the numerical solution of integral equations
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A section on nonlinear partial differential equations (PDEs) in the last chapter
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Inclusion of MATLAB GUIs throughout the text
The book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization. They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs.
CD-ROM Resource
The accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm.
Written in an easy-to-follow, simple style, this text improves students’ ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.
Chapter 1 : Introduction
Chapter 2 : Number System and Errors
Chapter 3 : Roots of Equations
Chapter 4 : System of Linear Equations
Chapter 5 : Interpolation
Chapter 6 : Interpolation with Spline Functions
Chapter 7 : The Method of Least Squares
Chapter 8 : Numerical Optimization
Chapter 9 : Numerical Differentiation
Chapter 10 : Numerical Integration
Chapter 11 : Numerical Methods for Linear Integral Equations
Chapter 12 : Numerical Methods for Differential Equations
Chapter 13 : Boundary-Value Problems
Chapter 14 : Eigenvalues and Eigenvectors
Chapter 15 : Partial Differential Equations
Bibliography
References
Appendix A : Calculus Review
Appendix B : MATLAB Built-in Functions
Appendix C : Text MATLAB Functions
Appendix D : MATLAB GUI
Answers to Selected Exercises
Index
