Applied Numerical Methods with MATLAB for Engineers and Scientists

Cover
Title
Copyright
Contents
About the author
Preface
Part One: Modeling, Computers, and Error Analysis
	1.1 Motivation
	1.2 Part Organization
	Chapter 1 Mathematical Modeling, Numerical Methods, and Problem Solving
		1.1 A Simple Mathematical Model
		1.2 Conservation Laws in Engineering and Science
		1.3 Numerical Methods Covered in This Book
		1.4 Case Study: It's a Real Drag
		Problems
	Chapter 2 MATLAB Fundamentals
		2.1 The MATLAB Environment
		2.2 Assignment
		2.3 Mathematical Operations
		2.4 Use of Built-In Functions
		2.5 Graphics
		2.6 Other Resources
		2.7 Case Study: Exploratory Data Analysis
		Problems
	Chapter 3 Programming with MATLAB
		3.1 M-Files
		3.2 Input-Output
		3.3 Structured Programming
		3.4 Nesting and Indentation
		3.5 Passing Functions to M-Files
		3.6 Case Study: Bungee Jumper Velocity
		Problems
	Chapter 4 Roundoff and Truncation Errors
		4.1 Errors
		4.2 Roundoff Errors
		4.3 Truncation Errors
		4.4 Total Numerical Error
		4.5 Blunders, Model Errors, and Data Uncertainty
		Problems
Part Two: Roots and Optimization
	2.1 Overview
	2.2 Part Organization
	Chapter 5 Roots: Bracketing Methods
		5.1 Roots in Engineering and Science
		5.2 Graphical Methods
		5.3 Bracketing Methods and Initial Guesses
		5.4 Bisection
		5.5 False Position
		5.6 Case Study: Greenhouse Gases and Rainwater
		Problems
	Chapter 6 Roots: Open Methods
		6.1 Simple Fixed-Point Iteration
		6.2 Newton-Raphson
		6.3 Secant Methods
		6.4 Brent's Method
		6.5 MATLAB Function: fzero
		6.6 Polynomials
		6.7 Case Study: Pipe Friction
		Problems
	Chapter 7 Optimization
		7.1 Introduction and Background
		7.2 One-Dimensional Optimization
		7.3 Multidimensional Optimization
		7.4 Case Study: Equilibrium and Minimum Potential Energy
		Problems
Part Three: Linear Systems
	3.1 Overview
	3.2 Part Organization
	Chapter 8 Linear Algebraic Equations and Matrices
		8.1 Matrix Algebra Overview
		8.2 Solving Linear Algebraic Equations with MATLAB
		8.3 Case Study: Currents and Voltages in Circuits
		Problems
	Chapter 9 Gauss Elimination
		9.1 Solving Small Numbers of Equations
		9.2 Naive Gauss Elimination
		9.3 Pivoting
		9.4 Tridiagonal Systems
		9.5 Case Study: Model of a Heated Rod
		Problems
	Chapter 10 LU Factorization
		10.1 Overview of LU Factorization
		10.2 Gauss Elimination as LU Factorization
		10.3 Cholesky Factorization
		10.4 MATLAB Left Division
		Problems
	Chapter 11 Matrix Inverse and Condition
		11.1 The Matrix Inverse
		11.2 Error Analysis and System Condition
		11.3 Case Study: Indoor Air Pollution
		Problems
	Chapter 12 Iterative Methods
		12.1 Linear Systems: Gauss-Seidel
		12.2 Nonlinear Systems
		12.3 Case Study: Chemical Reactions
		Problems
	Chapter 13 Eigenvalues
		13.1 Mathematical Background
		13.2 Physical Background
		13.3 The Power Method
		13.4 MATLAB Function: eig
		13.5 Case Study: Eigenvalues and Earthquakes
		Problems
Part Four: Curve Fitting
	4.1 Overview
	4.2 Part Organization
	Chapter 14 Linear Regression
		14.1 Statistics Review
		14.2 Random Numbers and Simulation
		14.3 Linear Least-Squares Regression
		14.4 Linearization of Nonlinear Relationships
		14.5 Computer Applications
		14.6 Case Study: Enzyme Kinetics
		Problems
	Chapter 15 General Linear Least-Squares and Nonlinear Regression
		15.1 Polynomial Regression
		15.2 Multiple Linear Regression
		15.3 General Linear Least Squares
		15.4 QR Factorization and the Backslash Operator
		15.5 Nonlinear Regression
		15.6 Case Study: Fitting Experimental Data
		Problems
	Chapter 16 Fourier Analysis
		16.1 Curve Fitting with Sinusoidal Functions
		16.2 Continuous Fourier Series
		16.3 Frequency and Time Domains
		16.4 Fourier Integral and Transform
		16.5 Discrete Fourier Transform (DFT)
		16.6 The Power Spectrum
		16.7 Case Study: Sunspots
		Problems
	Chapter 17 Polynomial Interpolation
		17.1 Introduction to Interpolation
		17.2 Newton Interpolating Polynomial
		17.3 Lagrange Interpolating Polynomial
		17.4 Inverse Interpolation
		17.5 Extrapolation and Oscillations
		Problems
	Chapter 18 Splines and Piecewise Interpolation
		18.1 Introduction to Splines
		18.2 Linear Splines
		18.3 Quadratic Splines
		18.4 Cubic Splines
		18.5 Piecewise Interpolation in MATLAB
		18.6 Multidimensional Interpolation
		18.7 Case Study: Heat Transfer
		Problems
Part Five: Integration and Differentiation
	5.1 Overview
	5.2 Part Organization
	Chapter 19 Numerical Integration Formulas
		19.1 Introduction and Background
		19.2 Newton-Cotes Formulas
		19.3 The Trapezoidal Rule
		19.4 Simpson's Rules
		19.5 Higher-Order Newton-Cotes Formulas
		19.6 Integration with Unequal Segments
		19.7 Open Methods
		19.8 Multiple Integrals
		19.9 Case Study: Computing Work with Numerical Integration
		Problems
	Chapter 20 Numerical Integration of Functions
		20.1 Introduction
		20.2 Romberg Integration
		20.3 Gauss Quadrature
		20.4 Adaptive Quadrature
		20.5 Case Study: Root-Mean-Square Current
		Problems
	Chapter 21 Numerical Differentiation
		21.1 Introduction and Background
		21.2 High-Accuracy Differentiation Formulas
		21.3 Richardson Extrapolation
		21.4 Derivatives of Unequally Spaced Data
		21.5 Derivatives and Integrals for Data with Errors
		21.6 Partial Derivatives
		21.7 Numerical Differentiation with MATLAB
		21.8 Case Study: Visualizing Fields
		Problems
Part six: Ordinary Differential Equations
	6.1 Overview
	6.2 Part Organization
	Chapter 22 Initial-Value Problems
		22.1 Overview
		22.2 Euler's Method
		22.3 Improvements of Euler's Method
		22.4 Runge-Kutta Methods
		22.5 Systems of Equations
		22.6 Case Study: Predator-Prey Models and Chaos
		Problems
	Chapter 23 Adaptive Methods and Stiff Systems
		23.1 Adaptive Runge-Kutta Methods
		23.2 Multistep Methods
		23.3 Stiffness
		23.4 MATLAB Application: Bungee Jumper with Cord
		23.5 Case Study: Pliny's Intermittent Fountain
		Problems
	Chapter 24 Boundary-Value Problems
		24.1 Introduction and Background
		24.2 The Shooting Method
		24.3 Finite-Difference Methods
		24.4 MATLAB Function: bvp4c
		Problems
Appendix A: Matlab Built-In Functions
Appendix B: Matlab M-File Functions
Appendix C: Introduction To Simulink
Bibliography
Index
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