Numerical Methods for Engineers and Scientists An Introduction with Applications Using MATLAB

ISBN-10: 0471734403
ISBN-13: 9780471734406
Edition: 2008
List price: $192.95
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Description: Following a unique approach, this innovative book integrates the learning of numerical methods with practicing computer programming and using software tools in applications. It covers the fundamentals while emphasizing the most essential methods  More...

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Book details

List price: $192.95
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/6/2007
Binding: Hardcover
Pages: 480
Size: 8.25" wide x 10.25" long x 1.00" tall
Weight: 2.046
Language: English

Following a unique approach, this innovative book integrates the learning of numerical methods with practicing computer programming and using software tools in applications. It covers the fundamentals while emphasizing the most essential methods throughout the pages. Readers are also given the opportunity to enhance their programming skills using MATLAB to implement algorithms. They'll discover how to use this tool to solve problems in science and engineering.

Preface
Introduction
Background
Representation of Numbers on a Computer
Errors in Numerical Solutions
Round-Off Errors
Truncation Errors
Total Error
Computers and Programming
Problems
Mathematical Background
Background
Concepts from Pre-Calculus and Calculus
Vectors
Operations with Vectors
Matrices and Linear Algebra
Operations with Matrices
Special Matrices
Inverse of a Matrix
Properties of Matrices
Determinant of a Matrix
Cramer's Rule and Solution of a System of Simultaneous Linear Equations
Norms
Ordinary Differential Equations (ODE)
Functions of Two or More Independent Variables
Definition of the Partial Derivative
Chain Rules
The Jacobian
Taylor Series Expansion of Functions
Taylor Series for a Function of One Variable
Taylor Series for a Function of Two Variables
Problems
Solving Nonlinear Equations
Background
Estimation of Errors in Numerical Solutions
Bisection Method
Regula Falsi Method
Newton's Method
Secant Method
Fixed-Point Iteration Method
Use of MATLAB Built-In Functions for Solving Nonlinear Equations
The fzero Command
The roots Command
Equations with Multiple Solutions
Systems of Nonlinear Equations
Newton's Method for Solving a System of Nonlinear Equations
Fixed-Point Iteration Method for Solving a System of Nonlinear Equations
Problems
Solving a System of Linear Equations
Background
Overview of Numerical Methods for Solving a System of Linear Algebraic Equations
Gauss Elimination Method
Potential Difficulties When Applying the Gauss Elimination Method
Gauss Elimination with Pivoting
Gauss-Jordan Elimination Method
LU Decomposition Method
LU Decomposition Using the Gauss Elimination Procedure
LU Decomposition Using Crout's Method
LU Decomposition with Pivoting
Inverse of a Matrix
Calculating the Inverse with the LU Decomposition Method
Calculating the Inverse Using the Gauss-Jordan Method
Iterative Methods
Jacobi Iterative Method
Gauss-Seidel Iterative Method
Use of MATLAB Built-In Functions for Solving a System of Linear Equations
Solving a System of Equations Using MATLAB's Left and Right Division
Solving a System of Equations Using MATLAB's Inverse Operation
MATLAB's Built-In Function for LU Decomposition
Additional MATLAB Built-In Functions
Tridiagonal Systems of Equations
Error, Residual, Norms, and Condition Number
Error and Residual
Norms and Condition Number
Ill-Conditioned Systems
Eigenvalues and Eigenvectors
The Basic Power Method
The Inverse Power Method
The Shifted Power Method
The QR Factorization and Iteration Method
Use of MATLAB Built-In Functions for Determining Eigenvalues and Eigenvectors
Problems
Curve Fitting and Interpolation
Background
Curve Fitting with a Linear Equation
Measuring How Good Is a Fit
Linear Least-Squares Regression
Curve Fitting with Nonlinear Equation by Writing the Equation in a Linear Form
Curve Fitting with Quadratic and Higher-Order Polynomials
Interpolation Using a Single Polynomial
Lagrange Interpolating Polynomials
Newton's Interpolating Polynomials
Piecewise (Spline) Interpolation
Linear Splines
Quadratic Splines
Cubic Splines
Use of MATLAB Built-In Functions for Curve Fitting and Interpolation
Curve Fitting with a Linear Combination of Nonlinear Functions
Problems
Numerical Differentiation
Background
Finite Difference Approximation of the Derivative
Finite Difference Formulas Using Taylor Series Expansion
Finite Difference Formulas of First Derivative
Finite Difference Formulas for the Second Derivative
Summary of Finite Difference Formulas for Numerical Differentiation
Differentiation Formulas Using Lagrange Polynomials
Differentiation Using Curve Fitting
Use of MATLAB Built-In Functions for Numerical Differentiation
Richardson's Extrapolation
Error in Numerical Differentiation
Numerical Partial Differentiation
Problems
Numerical Integration
Background
Overview of Approaches in Numerical Integration
Rectangle and Midpoint Methods
Trapezoidal Method
Composite Trapezoidal Method
Simpson's Methods
Simpson's 1/3 Method
Simpson's 3/8 Method
Gauss Quadrature
Evaluation of Multiple Integrals
Use of MATLAB Built-In Functions for Integration
Estimation of Error in Numerical Integration
Richardson's Extrapolation
Romberg Integration
Improper Integrals
Integrals with Singularities
Integrals with Unbounded Limits
Problems
Ordinary Differential Equations: Initial- Value Problems
Background
Euler's Methods
Euler's Explicit Method
Analysis of Truncation Error in Euler's Explicit Method
Euler's Implicit Method
Modified Euler's Method
Midpoint Method
Runge-Kutta Methods
Second-Order Runge-Kutta Methods
Third-Order Runge-Kutta Methods
Fourth-Order Runge-Kutta Methods
Multistep Methods
Adams-Bashforth Method
Adams-Moulton Method
Predictor-Corrector Methods
System of First-Order Ordinary Differential Equations
Solving a System of First-Order ODEs Using Euler's Explicit Method
Solving a System of First-Order ODEs Using Second-Order Runge-Kutta Method (Modified Euler Version)
Solving a System of First-Order ODEs Using the Classical Fourth-Order Runge-Kutta Method
Solving a Higher-Order Initial Value Problem
Use of MATLAB Built-In Functions for Solving Initial-Value Problems
Solving a Single First-Order ODE Using MATLAB
Solving a System of First-Order ODEs Using MATLAB
Local Truncation Error in Second-Order Range-Kutta Method
Step Size For Desired Accuracy
Stability
Stiff Ordinary Differential Equations
Problems
Ordinary Differential Equations: Boundary-Value Problems
Background
The Shooting Method
Finite Difference Method
Use of MATLAB Built-In Functions for Solving Boundary Value Problems
Error and Stability in Numerical Solution of Boundary Value Problems
Problems
Introductory MATLAB
Background
Starting with MATLAB
Arrays
Mathematical Operations with Arrays
Script Files
Function Files
Programming in MATLAB
Relational and Logical Operators
Conditional Statements, if-else Structures
Loops
Plotting
Problems
MATLAB Programs
Index

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