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Applied Numerical Methods with MATLAB is designed to support a one-semester course in numerical methods. It has been written for students who want to learn and apply numerical methods in order to solve problems in engineering and science. As such, the methods are motivated by problems rather than by mathematics. That said, sufficient theory is provided so students come away with insight into the techniques and their shortcomings. This title will be available in Connect, featuring SmartBook, the MHeBook, and homework problems. Instructor Resources available for this title include: Image Library, Instructor Solutions Manual, Lecture PowerPoints, and MatLab Files. Cover Title Page Copyright Page Dedications About the Author Contents 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 The Wegstein Method 6.3 Newton-Raphson 6.4 Secant Methods 6.5 Brent’s Method 6.6 MATLAB Function: fzero 6.7 Polynomials 6.8 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 Eigenvalues and Eigenvectors—The Basics 13.2 Applications of Eigenvalues and Eigenvectors 13.3 Physical Settings—Mass-Spring Systems 13.4 The Power Method 13.5 MATLAB Function: eig 13.6 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 Smoothing of Data Series 18.8 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 Tangent Line Differentiation of Functions 21.5 Derivatives of Unequally Spaced Data 21.6 Differentiation of Noisy Data 21.7 Partial Derivatives 21.8 Numerical Differentiation with MATLAB 21.9 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