Ⅰ Understanding Problem Solving 1
1 Understanding Word Problems 3
1.1 Introduction 3
1.2 Nouns and Verbs 4
1.3 Problem Decomposition 6
1.4 The Language of Computational Problems 8
1.4.1 Terms for Computed Values 8
1.4.2 Implied Phrases 9
1.4.3 Units of Measure 9
1.4.4 Conditions 11
1.4.5 Repetition 13
1.5 Objects 14
1.6 Problems with Many Numbers 15
1.6.1 Working with Patterns 16
1.7 Summary 17
Key Terms 17
Exercises 18
2 Problem Solving and Computing 21
2.1 Introduction 21
2.2 Programs 21
2.3 Data Definitions 22
2.3.1 Name of Data Items 22
2.3.2 Data Types 23
2.3.3 Data Declarations 24
2.4 Programming Languages 24
2.4.1 High-Level Programming Languages 24
2.4.2 Interpreters 25
2.4.3 Compilers 25
2.4.4 Compiling and Execution of Java Programs 25
2.4.5 Compiling and Executing C＋＋ Programs 26
2.5 Interpretation of Commands with MATLAB？and Octave 27
2.6 Computer Problem Solving 28
2.7 Summary 30
Key Terms 31
Exercises 31
3 MATLAB and Octave Programming 33
3.1 Introduction 33
3.2 The MATLAB and Octave Prompt 33
3.3 Variables and Constants 35
3.4 Assignment Statements 35
3.5 Simple Mathematical Expressions 36
3.6 Scientific Notation 37
3.7 Built-In Mathematical Functions 37
3.8 Internal Documentation 38
3.9 Summary 39
Key Terms 39
Exercises 39
Ⅱ Computational Models 41
4 Introduction to Computational Models 43
4.1 Introduction 43
4.2 Preliminary Concepts 43
4.3 A Simple Problem：Temperature Conversion 46
4.3.1 Initial Problem Statement 46
4.3.2 Analysis and Conceptual Model 46
4.3.3 The Mathematical Model 47
4.4 Using MATLAB and Octave 48
4.4.1 Basic MATLAB and Octave Commands 48
4.4.2 The Computational Model 48
4.4.3 Using Data Lists with MATLAB and Octave 50
4.4.4 Implementation of Model with Data Lists 53
4.5 Summary 55
Key Terms 56
Exercises 56
5 Computational Models and Simulation 57
5.1 Introduction 57
5.2 Categories of Computational Models 57
5.3 Development of Computational Models 59
5.4 Simulation：Basic Concepts 61
5.4.1 Simulation Models 62
5.4.2 Simulation Results 64
5.5 Modular Decomposition 64
5.6 Average and Instantaneous Rate of Change 65
5.7 Area under a Curve 67
5.8 The Free-Falling Object 68
5.8.1 Initial Problem Statement 69
5.8.2 Analysis and Conceptual Model 69
5.8.2.1 Assumptions 70
5.8.2.2 Basic Definitions 70
5.8.3 The Mathematical Model 70
5.8.4 The Computational Model 71
5.8.4.1 Simple Implementation 71
5.8.4.2 Implementation with Arrays 75
5.8.4.3 Computing the Rates of Change 78
5.9 Summary 79
Key Terms 80
Exercises 80
6 Algorithms and Design Structures 83
6.1 Introduction 83
6.2 Problem Solving 83
6.3 Algorithms 84
6.4 Describing Data 84
6.5 Notations for Describing Algorithms 85
6.5.1 Flowcharts 85
6.5.2 Pseudo-Code 86
6.6 Algorithmic Structures 87
6.6.1 Sequence 88
6.6.2 Selection 88
6.6.3 Repetition 88
6.7 Implementation of Algorithms 90
6.7.1 Programming Languages 91
6.7.2 Assignment and Arithmetic Expressions 92
6.7.3 Simple Numeric Computations 92
6.7.4 Simple Input/Output 93
6.8 Computing Area and Circumference 95
6.8.1 Specification 95
6.8.2 Algorithm with the Mathematical Model 95
6.9 Summary 97
Key Terms 97
Exercises 97
7 Selection 99
7.1 Introduction 99
7.2 Selection Structure 99
7.2.1 General Concepts of the Selection Structure 99
7.2.2 Selection with Pseudo-Code 100
7.2.3 Selection with MATLAB and Octave 101
7.2.4 Conditional Expressions 101
7.2.5 Example with Selection 102
7.3 Complex Numbers with MATLAB and Octave 104
7.4 A Computational Model with Selection 106
7.4.1 Analysis and Mathematical Model 106
7.4.2 Algorithm for General Solution 106
7.4.3 Detailed Algorithm 107
7.5 Multilevel Selection 109
7.5.1 General Multipath Selection 110
7.5.2 The Case Structure 111
7.6 Complex Conditions 113
7.7 Summary 114
Key Terms 114
Exercises 115
8 Repetition 117
8.1 Introduction 117
8.2 Repetition with While Construct 117
8.2.1 While-Loop Flowchart 118
8.2.2 The While Structure in Pseudo-Code 118
8.2.3 While-Loop with MATLAB and Octave 119
8.2.4 Loop Counter 119
8.2.5 Accumulator Variables 120
8.2.6 Summation of Input Numbers 121
8.3 Repeat-Until Construct 122
8.4 For Loop Structure 124
8.4.1 The Summation Problem with a For Loop 125
8.4.2 The Factorial Problem 126
8.4.2.1 Mathematical Specification of Factorial 126
8.4.2.2 Computing Factorial 126
8.5 Summary 127
Key Terms 128
Exercises 128
9 Data Lists 131
9.1 Introduction 131
9.2 Creating an Array 132
9.2.1 Creating Arrays in Pseudo-Code 132
9.2.2 Creating Arrays in MATLAB and Octave 133
9.3 Operations on Arrays 135
9.3.1 Array Elements in Pseudo-Code 136
9.3.2 Using Array Elements with MATLAB and Octave 136
9.3.3 Arithmetic Operations on Vectors 137
9.4 Multidimensional Arrays 138
9.4.1 Multidimensional Arrays with Pseudo-Code 138
9.4.2 Multidimensional Arrays with MATLAB and Octave 139
9.5 Applications Using Arrays 141
9.5.1 Problems with Simple Array Manipulation 141
9.5.1.1 The Average Value in an Array 141
9.5.1.2 Maximum Value in an Array 143
9.5.2 Searching 145
9.5.2.1 Linear Search 145
9.5.2.2 Binary Search 147
9.6 Average and Instantaneous Rate of Change 150
9.6.1 Average Rate of Change 150
9.6.2 Instantaneous Rate of Change 151
9.6.3 Computing the Rates of Change 152
9.7 Area under a Curve 156
9.8 Summary 159
Key Terms 160
Exercises 160
10 Modules 163
10.1 Introduction 163
10.2 Modular Design 163
10.3 MATLAB and Octave Script Files 165
10.4 Functions 166
10.4.1 Function Definition 166
10.4.2 Function Definition in MATLAB and Octave 167
10.4.3 Simple Function Calls 168
10.4.4 Functions with Parameters 169
10.4.5 Function Calls with Data 170
10.4.6 Functions with Return Data 171
10.5 Documenting MATLAB and Octave Functions 172
10.6 Summary 173
Key Terms 173
Exercises 174
11 Mathematical Models：Basic Concepts 175
11.1 Introduction 175
11.2 From the Real-World to the Abstract World 175
11.3 Discrete and Continuous Models 177
11.4 Difference Equations and Data Lists 177
11.5 Functional Equations 180
11.6 Validating a Model 181
11.7 Models with Arithmetic Growth 181
11.8 Using MATLAB and Octave to Implement the Model 182
11.8.1 MATLAB and Octave Implementation 182
11.8.2 Producing the Charts of the Model 183
11.9 Summary 185
Key Terms 185
Exercises 186
12 Models with Quadratic Growth 187
12.1 Introduction 187
12.2 Quadratic Growth 187
12.3 Differences of the Data 188
12.4 Difference Equations 191
12.5 Functional Equations 192
12.6 Models with Quadratic Growth 193
12.6.1 Simple Quadratic Growth Models 193
12.6.2 Models with Sums of Arithmetic Growth 194
12.7 Solution and Graphs of Quadratic Equations 196
12.8 Summary 198
Key Terms 198
Exercises 198
13 Models with Polynomial Functions 201
13.1 Introduction 201
13.2 General Forms of Polynomial Functions 201
13.3 Evaluation and Graphs of Polynomial Functions 202
13.3.1 Evaluating Polynomial Functions 202
13.3.2 Generating Graphs of Polynomial Functions 205
13.4 Solution to Polynomial Equations 206
13.5 Summary 209
Key Terms 209
Exercises 209
14 Data Estimation and Empirical Modeling 211
14.1 Introduction 211
14.2 Interpolation 211
14.2.1 Linear Interpolation 212
14.2.2 Nonlinear Interpolation 215
14.3 Curve Fitting 218
14.4 Summary 220
Key Terms 221
Exercises 221
15 Models with Geometric Growth 225
15.1 Introduction 225
15.2 Basic Concepts of Geometric Growth 225
15.2.1 Geometric Growth with Increasing Data 226
15.2.2 Geometric Growth with Decreasing Data 226
15.2.3 Geometric Growth：Case Study 1 227
15.2.4 Geometric Growth：Case Study 2 230
15.3 Functional Equations in Geometric Growth 232
15.4 Properties of Exponential Functions 233
15.4.1 Exponentiation 233
15.4.2 Logarithms 233
15.5 Summary 236
Key Terms 236
Exercises 236
16 Vectors and Matrices 239
16.1 Introduction 239
16.2 Vectors 240
16.3 Simple Vector Operations 240
16.3.1 Arithmetic Operations 241
16.3.2 Applying Vector Functions 243
16.4 Matrices 245
16.4.1 Arithmetic Operations 246
16.4.2 Function Application 247
16.5 Array Indexing 247
16.6 Plotting Vectors 249
16.7 Summary 251
Key Terms 251
Exercises 251
17 Text Data 253
17.1 Introduction 253
17.2 String Vectors 253
17.2.1 String Operations 253
17.2.2 String Functions 254
17.3 String Matrices 257
17.4 Summary 258
Key Terms 258
Exercises 258
18 Advanced Data Structures 259
18.1 Introduction 259
18.2 Cell Arrays 259
18.3 Structures 264
18.4 Summary 268
Key Terms 268
Exercises 268
Appendix A MATLAB and GNU Octave Software 271
A.1 Introduction 271
A.2 The MATLAB Components 271
A.3 The Desktop 272
A.4 Starting MATLAB 274
A.5 Exiting MATLAB 274
A.6 The Command Window 275
A.7 Current User Folder 275
A.8 The Startup Folder 276
A.9 Using Command Files（Scripts） 276
A.10 MATLAB Functions 280
A.11 GNU Octave 285
Appendix B Computer Systems 289
B.1 Introduction 289
B.2 Computer Systems 289
B.2.1 Hardware Components 290
B.2.1.1 Processors 290
B.2.1.2 Main Memory 291
B.2.1.3 Storage Devices 291
B.2.1.4 Input Devices 292
B.2.1.5 Output Devices 292
B.2.1.6 Bus 292
B.2.2 Computer Networks 292
B.2.3 Software Components 293
B.3 Operating Systems 294
B.3.1 Operating System User Interfaces 294
B.3.2 Contemporary Operating Systems 295
B.3.2.1 Unix 295
B.3.2.2 Microsoft Windows 296
B.4 Summary 296
Key Terms 296
Bibliography 297
Index 299