Introduction to Mathematical Methods for Environmental Engineers and Scientists

<p>Preface ix</p>
<p>Part I: Introduction 1</p>
<p>1 Fundamentals and Principles of Numbers 3</p>
<p>2 Series Analysis 21</p>
<p>3 Graphical Analysis 29</p>
<p>4 Flow Diagrams 43</p>
<p>5 Dimensional Analysis 53</p>
<p>6 Economics 73</p>
<p>7 Problem Solving 89</p>
<p>Part II: Analytical Analysis 99</p>
<p>8 Analytical Geometry 101</p>
<p>9 Differentiation 115</p>
<p>10 Integration 121</p>
<p>11 Differential Calculus 133</p>
<p>12 Integral Calculus 147</p>
<p>13 Matrix Algebra 161</p>
<p>14 Laplace Transforms 173</p>
<p>Part III: Numerical Analysis 183</p>
<p>15 Trial–and–Error Solutions 185</p>
<p>16 Nonlinear Algebraic Equations 195</p>
<p>17 Simultaneous Linear Algebraic Equations 209</p>
<p>18 Differentiation 219</p>
<p>19 Integration 225</p>
<p>20 Ordinary Differential Equations 235</p>
<p>21 Partial Differential Equations 247</p>
<p>Part IV: Statistical Analysis 259</p>
<p>22 Basic Probability Concepts 261</p>
<p>23 Estimation of Mean and Variance 275</p>
<p>24 Discrete Probability Distribution 287</p>
<p>25 Continuous Probability Distribution 307</p>
<p>26 Fault Tree and Event Tree Analysis 343</p>
<p>27 Monte Carlo Simulation 357</p>
<p>28 Regression Analysis 371</p>
<p>Part V: Optimization 385</p>
<p>29 Introduction to Optimization 387</p>
<p>30 Perturbation Techniques 395</p>
<p>31 Search Methods 405</p>
<p>32 Graphical Analysis 419</p>
<p>33 Analytical Analysis 435</p>
<p>34 Introduction to Linear Programming 449</p>
<p>35 Linear Programming Applications 465</p>