Numerical Methods for Engineers and Scientists Using MATLAB®, Second Edition.

✍ Scribed by Esfandiari, Ramin S.

• Publisher: Chapman and Hall/CRC
• Year: 2017
• Tongue: English
• Leaves: 495
• Edition: 2nd ed.
• Category: Library

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication Page
Contents
Preface
Acknowledgments
Author
1. Background and Introduction
Part 1: Background
1.1 Differential Equations
1.1.1 Linear, First-Order ODEs
1.1.2 Second-Order ODEs with Constant Coefficients
1.1.2.1 Homogeneous Solution
1.1.2.2 Particular Solution
1.1.3 Method of Undetermined Coefficients
1.2 Matrix Analysis
1.2.1 Matrix Operations
1.2.2 Matrix Transpose
1.2.3 Special Matrices
1.2.4 Determinant of a Matrix
1.2.5 Properties of Determinant
1.2.5.1 Cramer's Rule
1.2.6 Inverse of a Matrix. 1.2.7 Properties of Inverse1.2.8 Solving a Linear System of Equations
1.3 Matrix Eigenvalue Problem
1.3.1 Solving the Eigenvalue Problem
1.3.2 Similarity Transformation
1.3.3 Matrix Diagonalization
1.3.4 Eigenvalue Properties of Matrices
Part 2: Introduction to Numerical Methods
1.4 Errors and Approximations
1.4.1 Sources of Computational Error
1.4.2 Binary and Hexadecimal Numbers
1.4.3 Floating Point and Rounding Errors
1.4.4 Round-Off: Chopping and Rounding
1.4.5 Absolute and Relative Errors
1.4.6 Error Bound
1.4.7 Transmission of Error from a Source to the Final Result. 1.4.8 Subtraction of Nearly Equal Numbers1.5 Iterative Methods
1.5.1 Fundamental Iterative Method
1.5.2 Rate of Convergence of an Iterative Method
Problem Set (Chapter 1)
2. Introduction to MATLAB®
2.1 MATLAB Built-In Functions
2.1.1 Rounding Commands
2.1.2 Relational Operators
2.1.3 Format Options
2.2 Vectors and Matrices
2.2.1 Linspace
2.2.2 Matrices
2.2.3 Determinant, Transpose, and Inverse
2.2.4 Slash Operators
2.2.5 Element-by-Element Operations
2.2.6 Diagonal Matrices and Diagonals of a Matrix
2.3 Symbolic Math Toolbox
2.3.1 Anonymous Functions
2.3.2 MATLAB Function. 2.3.3 Differentiation2.3.4 Partial Derivatives
2.3.5 Integration
2.4 Program Flow Control
2.4.1 for Loop
2.4.2 The if Command
2.4.3 while Loop
2.5 Displaying Formatted Data
2.5.1 Differential Equations
2.6 Plotting
2.6.1 subplot
2.6.2 Plotting Analytical Expressions
2.6.3 Multiple Plots
2.7 User-Defined Functions and Script Files
2.7.1 Setting Default Values for Input Variables
2.7.2 Creating Script Files
Problem Set (Chapter 2)
3. Numerical Solution of Equations of a Single Variable
3.1 Numerical Solution of Equations
3.2 Bisection Method. 3.2.1 MATLAB Built-In Function fzero3.3 Regula Falsi Method (Method of False Position)
3.3.1 Modified Regula Falsi Method
3.4 Fixed-Point Method
3.4.1 Selection of a Suitable Iteration Function
3.4.2 A Note on Convergence
3.4.3 Rate of Convergence of the Fixed-Point Iteration
3.5 Newton's Method (Newton-Raphson Method)
3.5.1 Rate of Convergence of Newton's Method
3.5.2 A Few Notes on Newton's Method
3.5.3 Modified Newton's Method for Roots with Multiplicity 2 or Higher
3.6 Secant Method
3.6.1 Rate of Convergence of Secant Method
3.6.2 A Few Notes on Secant Method.