# Applied Numerical Methods with MATLAB

(Parte 1 de 16)

About the Aufhor iv Prefoce xiii Guided Tour xvii

Panr Our Modeling, Computers, ond Error Anolysis I l. I Motivofion I 1.2 Port Orgonizotion 2

Mothemqticol Modeling, Numericol Methods, ond Problem Solving 4

I .l A Simple Mothemoticol Model 5 1 .2 Conservotion Lows in Engineering ond Science 12

1 .3 Numericol Methods Covered in This Book l3 Problems 17

CHAPTER 2

MATLAB Fundomeniqls 20

2.1 The MATIAB Environmenl 21 2.2 Assignment 2 2.3 Mothemoticol Operotions 27 2.4 Use of Builtln Functions 30 2.5 Groohics 3 2.6 Other Resources 36

2.7 Cose Study: Explorotory Doto Anolysis 37rroblems JY

CHAPTER 3

Progromming with MATTAB 42

3.1 M-Files 43 3.2 InputOutput 47 vl CONTENTS

3.3 Shuctured Progromming 5l

3.4 Nesting ond Indentotion 63 3.5 Possing Functions to M-Files 6

3.6 Cose Study: Bungee Jumper Velocity 71 Problems 75

CHAPTER 4

Roundoff qnd Truncotion Errors 79

4.1 Errors B0 4.2 Roundoff Errors 84

4.3 Truncotion Errors 92 4.4 Totol Numericol Error ,l03

4.5 Blunders, Model Errors, ond Doto Uncertointy 108Problems ,l09

Pnnr Two Roots ond Optimizotion .|1

2.1 Overview tll 2.2 Port Orgonizotion I 12

CHAPTER 5

Roois: Brocketing Methods I l4

5.1 Roots in Engineering ond Science I l5 5.2 Grophicol Methods I l6 5.3 Brocketing Methods ond Initiol Guesses 117 5.4 Bisection 122 5.5 Folse Position 128

5.6 Cose Studv: Greenhouse Goses ond Roinwoter 132Problems ,l35

CHAPTER 6

Roots: Open Methods | 39

6.1 Simple Fixed-Poini lterotion 6.2 Newton-Rophson 144 6.3 Secont Methods 149 6.4 MATLAB Function: f zero

6.5 Polvnomlols 154

6.6 Cose Study: Pipe Friction 157 Problems 162

CONTENTS Yrt

CHAPTER 7

Optimizofion 166

7.1 Introduciion ond Bockground 167 7.2 One-DimensionolOptimizotion 170 7.3 MultidimensionolOptimizotion 179 7.4 Cose Study: Equilibrium ond Minimum Potentiol Energy l8l Problems 183

Prnr Txnrr Lineor Systems ,|89

CHAPTER 8

3.1 Overview 189 3.2 Port Orgonizotion l9l

Lineqr Algebroic Equofions ond Motrices | 93

8.1 Motrix Algebro Overview 194 8.2 Solving Lineor Algebroic Equotions with MATLAB 203 8.3 Cose Study: Currents ond Voltoges in Circuits 205 Problems 209

CHAPTER 9

Gouss Eliminotion 212

9.1 Solving Smoll Numbers of Equotion s 213 9.2 Noive Gouss Eliminotion 218 9.3 Pivoting 225 9.4 Tridiogonol Systems 227

9.5 Cose Study: Model of o Heoted Rod 229 Problems 233

[U Foctorizotion 236 l0.l Overview of lU Foctorizotion 237 10.2 Gouss Eliminotion os lU Foctorizotion 238

10.3 Cholesky Foctorizotion 244'l0.4 MATLAB Left Division 246 Problems 247 vIt! CONIENTS

Motrix lnverse ond Condition 249

1 i .l The Motrix lnverse 249 I I .2 Error Anolysis ond System Condition 253 I 1.3 Cose Study: Indoor Air Pollution 258 Problems 261

CHAPTER I2 Iterotive Methods 264 l2.l Lineor Systems: Gouss-Seidel 264,l2.2 Nonlineor Systems 270 12.3 Cose Studv: Chemicol Reoctions 277 Problems 279

Ptrnr Foun Curve Fitting 281

(Parte 1 de 16)