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.
- Provides fully worked-out examples showing all details
- Confirms results through the execution of the user-defined function or the script file
- Executes built-in functions for re-confirmation, when available
- Generates plots regularly to shed light on the soundness and significance of the numerical results
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.
Table of Contents:
Background and Introduction
Background
Introduction to Numerical Methods
Problem Set
Introduction to MATLAB®
MATLAB® Built-In Functions
Vectors and Matrices
User-Defined Functions and Script Files
Program Flow Control
Displaying Formatted Data
Symbolic Toolbox
Plotting
Problem Set
Solution of Equations of a Single Variable
Numerical Solution of Equations
Bisection Method
Regula Falsi Method (Method of False Position)
Fixed-Point Method
Newton’s Method (Newton−Raphson Method)
Secant Method
Equations with Several Roots
Problem Set
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
Problem Set
Curve Fitting (Approximation) and Interpolation
Least-Squares Regression
Linear Regression
Linearization of Nonlinear Data
Polynomial Regression
Polynomial Interpolation
Spline Interpolation
Fourier Approximation and Interpolation
Problem Set
Numerical Differentiation and Integration
Numerical Differentiation
Finite-Difference Formulas for Numerical Differentiation
Numerical Integration: Newton–Cotes Formulas
Numerical Integration of Analytical Functions: Romberg Integration, Gaussian Quadrature
Improper Integrals
Problem Set
Numerical Solution of Initial-Value Problems
One-Step Methods
Euler’s Method
Runge–Kutta Methods
Multistep Methods
Systems of Ordinary Differential Equations
Stability
Stiff Differential Equations
MATLAB® Built-In Functions for Initial-Value Problems
Problem Set
Numerical Solution of Boundary-Value Problems
Shooting Method
Finite-Difference Method
BVPs with Mixed Boundary Conditions
MATLAB® Built-In Function bvp4c for BVPs
Problem Set
Matrix Eigenvalue Problem
Power Method: Estimation of the Dominant Eigenvalue
Deflation Methods
Householder Tridiagonalization and QR Factorization Methods
Problem Set
Numerical Solution of Partial Differential Equations
Introduction
Elliptic PDEs
Parabolic PDEs
Hyperbolic PDEs
Problem Set
Bibliography
Index
About the Author :
Dr. Ramin S. Esfandiari is a professor of mechanical and aerospace engineering at California State University, Long Beach. He received his BS in mechanical engineering, as well as his MA and PhD in applied mathematics from the University of California, Santa Barbara. He has authored several books and refereed research papers in high-quality engineering and scientific journals, including Modeling and Analysis of Dynamic Systems (CRC Press, 2010) with Dr. Bei Lu. Dr. Esfandiari has received several teaching and research awards, including two Meritorious Performance and Professional Promise Awards, the TRW Excellence in Teaching and Scholarship Award, and the Distinguished Faculty Teaching Award.
Review :
"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
