© 2013 – CRC Press
550 pages | 371 B/W Illus.
Designed to benefit scientific and engineering applications, Numerical Methods for Engineers and Scientists Using MATLAB® focuses on the fundamentals of numerical methods while making use of MATLAB software. The book introduces MATLAB early on and incorporates it throughout the chapters to perform symbolic, graphical, and numerical tasks. The text covers a variety of methods from curve fitting to solving ordinary and partial differential equations.
Created to be user-friendly and easily understandable, Numerical Methods for Engineers and Scientists Using MATLAB® provides background material and a broad introduction to the essentials of MATLAB, specifically its use with numerical methods. Building on this foundation, it introduces techniques for solving equations and focuses on curve fitting and interpolation techniques. It addresses numerical differentiation and integration methods, presents numerical methods for solving initial-value and boundary-value problems, and discusses the matrix eigenvalue problem, which entails numerical methods to approximate a few or all eigenvalues of a matrix. The book then deals with the numerical solution of partial differential equations, specifically those that frequently arise in engineering and science.
The book presents a user-defined function or a MATLAB script file for each method, followed by at least one fully worked-out example. When available, MATLAB built-in functions are executed for confirmation of the results. A large set of exercises of varying levels of difficulty appears at the end of each chapter. The concise approach with strong, up-to-date MATLAB integration provided by this book affords readers a thorough knowledge of the fundamentals of numerical methods utilized in various disciplines.
"Overall, this book provides the reader with a fundamental knowledge of basic numerical methods that are used in various disciplines in engineering and science. MATLAB is used throughout the book either in the implementation of a numerical method or in the completion of a homework problem. It covers a variety of numerical methods… "
––Zhangxing (John) Chen, University of Calgary, Alberta, Canada
"An excellent book for beginners, intermediate and professional users. The author has done an excellent job in explaining the concepts in simple and straightforward manner. The text is very complete, includes lots of worked out examples. I highly recommend this book to engineers, undergraduate and graduate students. A very good mix of mathematical theory and MATLAB applications."
—Alireza Tabarraei, Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte
Background and Introduction
Introduction to Numerical Methods
Introduction to MATLAB®
MATLAB® Built-In Functions
Vectors and Matrices
User-Defined Functions and Script Files
Program Flow Control
Displaying Formatted Data
Solution of Equations of a Single Variable
Numerical Solution of Equations
Regula Falsi Method (Method of False Position)
Newton’s Method (Newton−Raphson Method)
Equations with Several Roots
Solution of Systems of Equations
Linear Systems of Equations
Numerical Solution of Linear Systems
Gauss Elimination Method
LU Factorization Methods
Iterative Solution of Linear Systems
Ill-Conditioning and Error Analysis
Systems of Nonlinear Equations
Curve Fitting (Approximation) and Interpolation
Linearization of Nonlinear Data
Fourier Approximation and Interpolation
Numerical Differentiation and Integration
Finite-Difference Formulas for Numerical Differentiation
Numerical Integration: Newton–Cotes Formulas
Numerical Integration of Analytical Functions: Romberg Integration, Gaussian Quadrature
Numerical Solution of Initial-Value Problems
Systems of Ordinary Differential Equations
Stiff Differential Equations
MATLAB® Built-In Functions for Initial-Value Problems
Numerical Solution of Boundary-Value Problems
BVPs with Mixed Boundary Conditions
MATLAB® Built-In Function bvp4c for BVPs
Matrix Eigenvalue Problem
Power Method: Estimation of the Dominant Eigenvalue
Householder Tridiagonalization and QR Factorization Methods
Numerical Solution of Partial Differential Equations