# Introduction to Mathematical Methods for Environmental Engineers and Scientists

• ID: 4531933
• Book
• 498 Pages
• John Wiley and Sons Ltd
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The authors′ aim is to offer the reader the fundamentals of numerous mathematical methods with accompanying practical environmental applications.

The material in this book addresses mathematical calculations common to both the environmental science and engineering professionals. It provides the reader with nearly 100 solved illustrative examples and the interrelationship between both theory and applications is emphasized in nearly all of the 35 chapters. One key feature of this book is that the solutions to the problems are presented in a stand–alone manner. Throughout the book, the illustrative examples are laid out in such a way as to develop the reader′s technical understanding of the subject in question, with more difficult examples located at or near the end of each set.

In presenting the text material, the authors have stressed the pragmatic approach in the application of mathematical tools to assist the reader in grasping the role of mathematical skills in environmental problem–solving situations. The book is divided up into 5 parts:

• Introduction; Analytical Analysis; Numerical Analysis; Statistical Analysis; and Optimization.
• The analytical analysis includes graphical, trial–and–error, search, etc. methods.
• The numerical analysis includes integration, differentiation, differential equation, Monte Carlo, etc.
• The statistical analysis includes probability, probability distribution, decision trees, regression analysis, etc.
• Optimization includes both traditional approaches and linear programming.

Audience

This book serves two main audiences: As a reference book for practicing environmental engineers, environmental scientists, and technicians involved with the environment; it may also be used as a textbook for beginning environmental students.

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Preface ix

Part I: Introduction 1

1 Fundamentals and Principles of Numbers 3

2 Series Analysis 21

3 Graphical Analysis 29

4 Flow Diagrams 43

5 Dimensional Analysis 53

6 Economics 73

7 Problem Solving 89

Part II: Analytical Analysis 99

8 Analytical Geometry 101

9 Differentiation 115

10 Integration 121

11 Differential Calculus 133

12 Integral Calculus 147

13 Matrix Algebra 161

14 Laplace Transforms 173

Part III: Numerical Analysis 183

15 Trial–and–Error Solutions 185

16 Nonlinear Algebraic Equations 195

17 Simultaneous Linear Algebraic Equations 209

18 Differentiation 219

19 Integration 225

20 Ordinary Differential Equations 235

21 Partial Differential Equations 247

Part IV: Statistical Analysis 259

22 Basic Probability Concepts 261

23 Estimation of Mean and Variance 275

24 Discrete Probability Distribution 287

25 Continuous Probability Distribution 307

26 Fault Tree and Event Tree Analysis 343

27 Monte Carlo Simulation 357

28 Regression Analysis 371

Part V: Optimization 385

29 Introduction to Optimization 387

30 Perturbation Techniques 395

31 Search Methods 405

32 Graphical Analysis 419

33 Analytical Analysis 435

34 Introduction to Linear Programming 449

35 Linear Programming Applications 465

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