Numerical Methods for Engineers and Scientists Using MATLAB®

Numerical Methods for Engineers and Scientists Using MATLAB®

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Features

    • Introduces MATLAB at the outset and uses it to perform symbolic, graphical, and numerical tasks
    • Covers a wide array of methods, from curve fitting to solving ordinary and partial differential equations
    • Accompanies each method with either a user-defined function or a MATLAB script file
    • Gives a comprehensive introduction to the essentials of MATLAB for numerical methods

    Summary

    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

    Author Bio(s)

    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.

    Editorial Reviews

    "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

    "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

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    MATLAB Functions.zip Cross Platform February 04, 2014

     
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