The material in this book attempts to address mathematical calculations common to both the environmental science and engineering professionals. The book provides the reader with nearly 100 solved illustrative examples. 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 five (V) parts:

1. Introduction
2. Analytical Analysis
3. Numerical Analysis
4. Statistical Analysis

Charles Prochaska is a graduate student at Manhattan College pursuing a M.S. degree in chemical engineering. He is currently working in pre-clinical manufacturing process development at Regeneron Pharmaceuticals.Before exploring chemical engineering, Charles worked as a cosmetics chemist and procedure consultant for three years. Charles researched biomolecule-nanoparticle interactions for the Center for Functional Nanomaterials located in Brookhaven National Laboratory as well as novel DNA nanotag development at St. Joseph's College.

Louis Theodore, MChE and EngScD, is a retired professor of chemical engineering (50 years). He is the author of several publications, including Fluid Flow for the Practicing Chemical Engineer, Thermodynamics for the Practicing Engineer, Mass Transfer Operations for the Practicing Engineer, and Air Pollution Control Equipment Calculations. Dr. Theodore is also a contributor to Perry's Chemical Engineers' Handbook.

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