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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.

**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

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.

**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

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.

**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

**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

**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.

**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

**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

**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.

**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

**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

**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.

**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