Preface |
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xiii | |
Authors |
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xvii | |
Chapter 1 Introduction To Computational Modeling |
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1 | (20) |
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1.1 The Importance Of Computational Science |
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1 | (2) |
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1.2 How Modeling Has Contributed To Advances In Science And Engineering |
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3 | (6) |
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1.2.1 Some Contemporary Examples |
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8 | (1) |
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9 | (8) |
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1.3.1 Steps In The Modeling Process |
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11 | (3) |
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1.3.2 Mathematical Modeling Terminology And Approaches To Simulation |
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14 | (1) |
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1.3.3 Modeling And Simulation Terminology |
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14 | (1) |
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1.3.4 Example Applications Of Modeling And Simulation |
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15 | (2) |
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17 | (1) |
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18 | (3) |
Chapter 2 Introduction To Programming Environments |
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21 | (24) |
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2.1 The Matlab® Programming Environment |
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21 | (9) |
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2.1.1 The Matlab® Interface |
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21 | (2) |
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23 | (5) |
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2.1.2.1 Variables And Operators |
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23 | (2) |
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25 | (1) |
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26 | (2) |
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28 | (1) |
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28 | (1) |
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2.1.5 Creating Repeatable Code |
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29 | (1) |
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30 | (1) |
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2.2 The Python Environment |
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30 | (12) |
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2.2.1 Recommendations And Installation |
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30 | (1) |
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2.2.2 The Spyder Interface |
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31 | (1) |
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32 | (6) |
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2.2.3.1 Variables And Operators |
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32 | (2) |
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34 | (1) |
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35 | (3) |
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38 | (1) |
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39 | (1) |
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40 | (1) |
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2.2.7 Creating Repeatable Code |
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40 | (1) |
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41 | (1) |
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42 | (3) |
Chapter 3 Deterministic Linear Models |
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45 | (10) |
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3.1 Selecting A Mathematical Representation For A Model |
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45 | (1) |
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3.2 Linear Models And Linear Equations |
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46 | (3) |
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49 | (2) |
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3.4 Systems Of Linear Equations |
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51 | (1) |
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3.5 Limitations Of Linear Models |
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51 | (1) |
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52 | (1) |
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53 | (2) |
Chapter 4 Array Mathematics In Matlab® And Python |
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55 | (6) |
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4.1 Introduction To Arrays And Matrices |
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55 | (1) |
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4.2 Brief Overview Of Matrix Mathematics |
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56 | (2) |
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4.3 Matrix Operations In Matlab® |
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58 | (1) |
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4.4 Matrix Operations In Python |
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59 | (1) |
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60 | (1) |
Chapter 5 Plotting |
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61 | (18) |
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61 | (7) |
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68 | (8) |
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76 | (3) |
Chapter 6 Problem Solving |
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79 | (8) |
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79 | (1) |
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6.2 Bottle Filling Example |
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80 | (1) |
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6.3 Tools For Program Development |
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81 | (3) |
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82 | (1) |
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82 | (1) |
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83 | (1) |
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6.4 Bottle Filling Example Continued |
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84 | (1) |
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85 | (2) |
Chapter 7 Conditional Statements |
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87 | (10) |
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87 | (1) |
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88 | (1) |
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7.3 Conditional Statements |
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89 | (6) |
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89 | (3) |
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92 | (3) |
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95 | (2) |
Chapter 8 Iteration And Loops |
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97 | (4) |
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97 | (2) |
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97 | (1) |
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98 | (1) |
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99 | (1) |
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8.2.1 Matlab® While Loops |
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99 | (1) |
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99 | (1) |
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100 | (1) |
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100 | (1) |
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100 | (1) |
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100 | (1) |
Chapter 9 Nonlinear And Dynamic Models |
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101 | (16) |
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9.1 Modeling Complex Systems |
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101 | (1) |
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101 | (10) |
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9.2.1 Components Of A System |
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102 | (2) |
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9.2.2 Unconstrained Growth And Decay |
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104 | (4) |
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9.2.2.1 Unconstrained Growth Exercises |
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106 | (2) |
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108 | (3) |
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9.2.3.1 Constrained Growth Exercise |
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110 | (1) |
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9.3 Modeling Physical And Social Phenomena |
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111 | (4) |
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9.3.1 Simple Model Of Tossed Ball |
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112 | (1) |
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9.3.2 Extending The Model |
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113 | (4) |
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9.3.2.1 Ball Toss Exercise |
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114 | (1) |
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115 | (2) |
Chapter 10 Estimating Models From Empirical Data |
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117 | (16) |
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10.1 Using Data To Build Forecasting Models |
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117 | (3) |
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10.1.1 Limitations Of Empirical Models |
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118 | (2) |
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10.2 Fitting A Mathematical Function To Data |
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120 | (11) |
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10.2.1 Fitting A Linear Model |
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122 | (3) |
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10.2.2 Linear Models With Multiple Predictors |
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125 | (1) |
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10.2.3 Nonlinear Model Estimation |
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126 | (21) |
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10.2.3.1 Limitations With Linear Transformation |
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130 | (1) |
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10.2.3.2 Nonlinear Fitting And Regression |
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130 | (1) |
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131 | (1) |
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131 | (1) |
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132 | (1) |
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132 | (1) |
Chapter 11 Stochastic Models |
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133 | (12) |
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133 | (1) |
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11.2 Creating A Stochastic Model |
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134 | (2) |
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11.3 Random Number Generators In Matlab® And Python |
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136 | (1) |
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11.4 A Simple Code Example |
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137 | (2) |
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11.5 Examples Of Larger Scale Stochastic Models |
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139 | (3) |
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142 | (1) |
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143 | (1) |
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143 | (2) |
Chapter 12 Functions |
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145 | (6) |
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145 | (2) |
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147 | (2) |
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12.2.1 Functions Syntax In Python |
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147 | (1) |
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148 | (1) |
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149 | (2) |
Chapter 13 Verification, Validation, And Errors |
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151 | (18) |
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151 | (1) |
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152 | (7) |
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13.2.1 Absolute And Relative Error |
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152 | (1) |
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153 | (1) |
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13.2.3 Truncation And Rounding Error |
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153 | (2) |
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13.2.4 Violating Numeric Associative And Distributive Properties |
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155 | (1) |
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13.2.5 Algorithms And Errors |
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155 | (4) |
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156 | (2) |
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13.2.5.2 Runge-Kutta Method |
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158 | (1) |
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13.2.6 Ode Modules In Matlab® And Python |
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159 | (1) |
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13.3 Verification And Validation |
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159 | (7) |
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13.3.1 History And Definitions |
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160 | (2) |
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13.3.2 Verification Guidelines |
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162 | (1) |
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13.3.3 Validation Guidelines |
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163 | (8) |
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13.3.3.1 Quantitative And Statistical Validation Measures |
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164 | (2) |
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13.3.3.2 Graphical Methods |
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166 | (1) |
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166 | (1) |
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167 | (2) |
Chapter 14 Capstone Projects |
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169 | (14) |
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169 | (1) |
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170 | (1) |
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14.3 Project Descriptions |
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171 | (10) |
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171 | (1) |
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172 | (2) |
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14.3.3 Population Dynamics Model |
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174 | (2) |
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176 | (2) |
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178 | (2) |
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14.3.6 Empirical Model Of Heart Disease Risk Factors |
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180 | (1) |
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14.3.7 Stochastic Model Of Traffic |
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180 | (1) |
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14.3.8 Other Project Options |
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181 | (1) |
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181 | (2) |
Index |
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