INTRODUCTION TO ELEMENTARY COMPUTATIONAL MODELING ESSENTIAL CONCEPTSPDF|Epub|txt|kindle电子书版本网盘下载

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Ⅰ Understanding Problem Solving1

1 Understanding Word Problems3

1.1 Introduction3

1.2 Nouns and Verbs4

1.3 Problem Decomposition6

1.4 The Language of Computational Problems8

1.4.1 Terms for Computed Values8

1.4.2 Implied Phrases9

1.4.3 Units of Measure9

1.4.4 Conditions11

1.4.5 Repetition13

1.5 Objects14

1.6 Problems with Many Numbers15

1.6.1 Working with Patterns16

1.7 Summary17

Key Terms17

Exercises18

2 Problem Solving and Computing21

2.1 Introduction21

2.2 Programs21

2.3 Data Definitions22

2.3.1 Name of Data Items22

2.3.2 Data Types23

2.3.3 Data Declarations24

2.4 Programming Languages24

2.4.1 High-Level Programming Languages24

2.4.2 Interpreters25

2.4.3 Compilers25

2.4.4 Compiling and Execution of Java Programs25

2.4.5 Compiling and Executing C＋＋ Programs26

2.5 Interpretation of Commands with MATLAB？and Octave27

2.6 Computer Problem Solving28

2.7 Summary30

Key Terms31

Exercises31

3 MATLAB and Octave Programming33

3.1 Introduction33

3.2 The MATLAB and Octave Prompt33

3.3 Variables and Constants35

3.4 Assignment Statements35

3.5 Simple Mathematical Expressions36

3.6 Scientific Notation37

3.7 Built-In Mathematical Functions37

3.8 Internal Documentation38

3.9 Summary39

Key Terms39

Exercises39

Ⅱ Computational Models41

4 Introduction to Computational Models43

4.1 Introduction43

4.2 Preliminary Concepts43

4.3 A Simple Problem：Temperature Conversion46

4.3.1 Initial Problem Statement46

4.3.2 Analysis and Conceptual Model46

4.3.3 The Mathematical Model47

4.4 Using MATLAB and Octave48

4.4.1 Basic MATLAB and Octave Commands48

4.4.2 The Computational Model48

4.4.3 Using Data Lists with MATLAB and Octave50

4.4.4 Implementation of Model with Data Lists53

4.5 Summary55

Key Terms56

Exercises56

5 Computational Models and Simulation57

5.1 Introduction57

5.2 Categories of Computational Models57

5.3 Development of Computational Models59

5.4 Simulation：Basic Concepts61

5.4.1 Simulation Models62

5.4.2 Simulation Results64

5.5 Modular Decomposition64

5.6 Average and Instantaneous Rate of Change65

5.7 Area under a Curve67

5.8 The Free-Falling Object68

5.8.1 Initial Problem Statement69

5.8.2 Analysis and Conceptual Model69

5.8.2.1 Assumptions70

5.8.2.2 Basic Definitions70

5.8.3 The Mathematical Model70

5.8.4 The Computational Model71

5.8.4.1 Simple Implementation71

5.8.4.2 Implementation with Arrays75

5.8.4.3 Computing the Rates of Change78

5.9 Summary79

Key Terms80

Exercises80

6 Algorithms and Design Structures83

6.1 Introduction83

6.2 Problem Solving83

6.3 Algorithms84

6.4 Describing Data84

6.5 Notations for Describing Algorithms85

6.5.1 Flowcharts85

6.5.2 Pseudo-Code86

6.6 Algorithmic Structures87

6.6.1 Sequence88

6.6.2 Selection88

6.6.3 Repetition88

6.7 Implementation of Algorithms90

6.7.1 Programming Languages91

6.7.2 Assignment and Arithmetic Expressions92

6.7.3 Simple Numeric Computations92

6.7.4 Simple Input/Output93

6.8 Computing Area and Circumference95

6.8.1 Specification95

6.8.2 Algorithm with the Mathematical Model95

6.9 Summary97

Key Terms97

Exercises97

7 Selection99

7.1 Introduction99

7.2 Selection Structure99

7.2.1 General Concepts of the Selection Structure99

7.2.2 Selection with Pseudo-Code100

7.2.3 Selection with MATLAB and Octave101

7.2.4 Conditional Expressions101

7.2.5 Example with Selection102

7.3 Complex Numbers with MATLAB and Octave104

7.4 A Computational Model with Selection106

7.4.1 Analysis and Mathematical Model106

7.4.2 Algorithm for General Solution106

7.4.3 Detailed Algorithm107

7.5 Multilevel Selection109

7.5.1 General Multipath Selection110

7.5.2 The Case Structure111

7.6 Complex Conditions113

7.7 Summary114

Key Terms114

Exercises115

8 Repetition117

8.1 Introduction117

8.2 Repetition with While Construct117

8.2.1 While-Loop Flowchart118

8.2.2 The While Structure in Pseudo-Code118

8.2.3 While-Loop with MATLAB and Octave119

8.2.4 Loop Counter119

8.2.5 Accumulator Variables120

8.2.6 Summation of Input Numbers121

8.3 Repeat-Until Construct122

8.4 For Loop Structure124

8.4.1 The Summation Problem with a For Loop125

8.4.2 The Factorial Problem126

8.4.2.1 Mathematical Specification of Factorial126

8.4.2.2 Computing Factorial126

8.5 Summary127

Key Terms128

Exercises128

9 Data Lists131

9.1 Introduction131

9.2 Creating an Array132

9.2.1 Creating Arrays in Pseudo-Code132

9.2.2 Creating Arrays in MATLAB and Octave133

9.3 Operations on Arrays135

9.3.1 Array Elements in Pseudo-Code136

9.3.2 Using Array Elements with MATLAB and Octave136

9.3.3 Arithmetic Operations on Vectors137

9.4 Multidimensional Arrays138

9.4.1 Multidimensional Arrays with Pseudo-Code138

9.4.2 Multidimensional Arrays with MATLAB and Octave139

9.5 Applications Using Arrays141

9.5.1 Problems with Simple Array Manipulation141

9.5.1.1 The Average Value in an Array141

9.5.1.2 Maximum Value in an Array143

9.5.2 Searching145

9.5.2.1 Linear Search145

9.5.2.2 Binary Search147

9.6 Average and Instantaneous Rate of Change150

9.6.1 Average Rate of Change150

9.6.2 Instantaneous Rate of Change151

9.6.3 Computing the Rates of Change152

9.7 Area under a Curve156

9.8 Summary159

Key Terms160

Exercises160

10 Modules163

10.1 Introduction163

10.2 Modular Design163

10.3 MATLAB and Octave Script Files165

10.4 Functions166

10.4.1 Function Definition166

10.4.2 Function Definition in MATLAB and Octave167

10.4.3 Simple Function Calls168

10.4.4 Functions with Parameters169

10.4.5 Function Calls with Data170

10.4.6 Functions with Return Data171

10.5 Documenting MATLAB and Octave Functions172

10.6 Summary173

Key Terms173

Exercises174

11 Mathematical Models：Basic Concepts175

11.1 Introduction175

11.2 From the Real-World to the Abstract World175

11.3 Discrete and Continuous Models177

11.4 Difference Equations and Data Lists177

11.5 Functional Equations180

11.6 Validating a Model181

11.7 Models with Arithmetic Growth181

11.8 Using MATLAB and Octave to Implement the Model182

11.8.1 MATLAB and Octave Implementation182

11.8.2 Producing the Charts of the Model183

11.9 Summary185

Key Terms185

Exercises186

12 Models with Quadratic Growth187

12.1 Introduction187

12.2 Quadratic Growth187

12.3 Differences of the Data188

12.4 Difference Equations191

12.5 Functional Equations192

12.6 Models with Quadratic Growth193

12.6.1 Simple Quadratic Growth Models193

12.6.2 Models with Sums of Arithmetic Growth194

12.7 Solution and Graphs of Quadratic Equations196

12.8 Summary198

Key Terms198

Exercises198

13 Models with Polynomial Functions201

13.1 Introduction201

13.2 General Forms of Polynomial Functions201

13.3 Evaluation and Graphs of Polynomial Functions202

13.3.1 Evaluating Polynomial Functions202

13.3.2 Generating Graphs of Polynomial Functions205

13.4 Solution to Polynomial Equations206

13.5 Summary209

Key Terms209

Exercises209

14 Data Estimation and Empirical Modeling211

14.1 Introduction211

14.2 Interpolation211

14.2.1 Linear Interpolation212

14.2.2 Nonlinear Interpolation215

14.3 Curve Fitting218

14.4 Summary220

Key Terms221

Exercises221

15 Models with Geometric Growth225

15.1 Introduction225

15.2 Basic Concepts of Geometric Growth225

15.2.1 Geometric Growth with Increasing Data226

15.2.2 Geometric Growth with Decreasing Data226

15.2.3 Geometric Growth：Case Study 1227

15.2.4 Geometric Growth：Case Study 2230

15.3 Functional Equations in Geometric Growth232

15.4 Properties of Exponential Functions233

15.4.1 Exponentiation233

15.4.2 Logarithms233

15.5 Summary236

Key Terms236

Exercises236

16 Vectors and Matrices239

16.1 Introduction239

16.2 Vectors240

16.3 Simple Vector Operations240

16.3.1 Arithmetic Operations241

16.3.2 Applying Vector Functions243

16.4 Matrices245

16.4.1 Arithmetic Operations246

16.4.2 Function Application247

16.5 Array Indexing247

16.6 Plotting Vectors249

16.7 Summary251

Key Terms251

Exercises251

17 Text Data253

17.1 Introduction253

17.2 String Vectors253

17.2.1 String Operations253

17.2.2 String Functions254

17.3 String Matrices257

17.4 Summary258

Key Terms258

Exercises258

18 Advanced Data Structures259

18.1 Introduction259

18.2 Cell Arrays259

18.3 Structures264

18.4 Summary268

Key Terms268

Exercises268

Appendix A MATLAB and GNU Octave Software271

A.1 Introduction271

A.2 The MATLAB Components271

A.3 The Desktop272

A.4 Starting MATLAB274

A.5 Exiting MATLAB274

A.6 The Command Window275

A.7 Current User Folder275

A.8 The Startup Folder276

A.9 Using Command Files（Scripts）276

A.10 MATLAB Functions280

A.11 GNU Octave285

Appendix B Computer Systems289

B.1 Introduction289

B.2 Computer Systems289

B.2.1 Hardware Components290

B.2.1.1 Processors290

B.2.1.2 Main Memory291

B.2.1.3 Storage Devices291

B.2.1.4 Input Devices292

B.2.1.5 Output Devices292

B.2.1.6 Bus292

B.2.2 Computer Networks292

B.2.3 Software Components293

B.3 Operating Systems294

B.3.1 Operating System User Interfaces294

B.3.2 Contemporary Operating Systems295

B.3.2.1 Unix295

B.3.2.2 Microsoft Windows296

B.4 Summary296

Key Terms296

Bibliography297

Index299