Cover Page

Scrivener Publishing
100 Cummings Center, Suite 541J
Beverly, MA 01915-6106

Publishers at Scrivener
Martin Scrivener (martin@scrivenerpublishing.com)
Phillip Carmical (pcarmical@scrivenerpublishing.com)

Introduction to Mathematical Methods for Environmental Engineers and Scientists

 

 

 

Charles Prochaska

Louis Theodore

 

 

 

 

Wiley Logo

To

my parents who have provided immeasurable
support in every aspect of my life (CP)

and

Arthur Lovely, a truly great guy and the world’s greatest
sports historian… ever (LT)

Preface

It is no secret that in recent years the number of people entering the environmental field has increased at a near exponential rate. Some are beginning college students and others had earlier chosen a non-technical major/career path. A large number of these individuals are today seeking technical degrees in environmental engineering or in the environmental sciences. These prospective students will require an understanding and appreciation of the numerous mathematical methods that are routinely employed in practice. This technical steppingstone to a successful career is rarely provided at institutions that award technical degrees. This introductory text on mathematical methods attempts to supplement existing environmental curricula with a sorely needed tool to eliminate this void.

The question often arises as to the educational background required for meaningful analysis capabilities since technology has changed the emphasis that is placed on certain mathematical subjects. Before computer usage became popular, instruction in environmental analysis was (and still is in many places) restricted to simple systems and most of the effort was devoted to solving a few derived elementary equations. These cases were mostly of academic interest, and because of their simplicity, were of little practical value. To this end, a considerable amount of time is now required to acquire skills in mathematics, especially in numerical methods, statistics, and optimization. In fact, most environmental engineers and scientists are given courses in classical mathematics, but experience shows that very little of this knowledge is retained after graduation for the simple reason that these mathematical methods are not adequate for solving most systems of equations encountered in industry. In addition, advanced mathematical skills are either not provided in courses or are forgotten through sheer disuse.

As noted in the above paragraph, the material in this book was prepared primarily for beginning environmental engineering and science students and, to a lesser extent, for environmental professionals who wish to obtain a better understanding of the various mathematical methods that can be employed in solving technical problems. The content is such that it is suitable both for classroom use and for individual study. 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.

In effect, this book serves two purposes. It may be used as a textbook for beginning environmental students or as a “reference” book for practicing engineers, scientists, and technicians involved with the environment. The authors have assumed that the reader has already taken basic courses in physics and chemistry, and should have a minimum background in mathematics through elementary calculus. The authors’ aim is to offer the reader the fundamentals of numerous mathematical methods with accompanying practical environmental applications. The reader is encouraged through references to continue his or her own development beyond the scope of the presented material.

As is usually the case in preparing any text, the question of what to include and what to omit has been particularly difficult. The material in this book attempts to address mathematical calculations common to both the environmental engineering and science 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 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.

The book is divided up into five (V) parts (see also the Table of Contents):

  1. I.     Introduction
  2. II.    Analytical Analysis
  3. III.  Numerical Analysis
  4. IV.  Statistical Analysis
  5. V.    Optimization

Most chapters contain a short introduction to the mathematical method in question, which is followed by developmental material, which in turn, is followed by one or more illustrative examples. Thus, this book offers material not only to individuals with limited technical background but also to those with extensive environmental industrial experience. As noted above, this book may be used as a text in either a general introductory environmental engineering/ science course and (perhaps) as a training tool in industry for challenged environmental professionals.

Hopefully, the text is simple, clear, to the point, and imparts a basic understanding of the theory and application of many of the mathematical methods employed in environmental practice. It should also assist the reader in helping master the difficult task of explaining what was once a very complicated subject matter in a way that is easily understood. The authors feel that this delineates this text from the numerous others in this field.

It should also be noted that the authors have long advocated that basic science courses – particularly those concerned with mathematics – should be taught to engineers and applied scientists by an engineer or applied scientist. Also, the books adopted for use in these courses should be written by an engineer or an applied scientist. For example, a mathematician will lecture on differentiation – say dx/dy – not realizing that in a real-world application involving an estuary y could refer to concentration while x could refer to time. The reader of this book will not encounter this problem.

The reader should also note that parts of the material in the book were drawn from one of the author’s notes of yesteryear. In a few instances, the original source was not available for referencing purposes. Any oversight will be corrected in a later printing/edition.

The authors wish to express appreciation to those who have contributed suggestions for material covered in this book. Their comments have been very helpful in the selection and presentation of the subject matter. Special appreciation is extended to Megan Menzel for her technical contributions and review, Dan McCloskey for preparing some of the first draft material in Parts II and III, and Christopher Testa for his contributions to Chapters 13 and 14. Thanks are also due to Rita D’Aquino, Mary K. Theodore, and Ronnie Zaglin.

Finally, the authors are especially interested in learning the opinions of those who read this book concerning its utility and serviceability in meeting the needs for which it was written. Corrections, improvements and suggestions will be considered for inclusion in later editions.

Chuck Prochaska
Lou Theodore
April 2018

Part I
INTRODUCTORY PRINCIPLES

Webster defines introduction as … “the preliminary section of a book, usually explaining or defining the subject matter …” And indeed, that is exactly what this Part I of the book is all about. The chapters contain material that one might view as a pre-requisite for the specific mathematical methods that are addressed in Parts II–V.

There are seven chapters in Part I. The chapter numbers and accompanying titles are listed below.

Chapter 1: Fundamentals and Principles of Numbers

Chapter 2: Series Analysis

Chapter 3: Graphical Analysis

Chapter 4: Flow Diagrams

Chapter 5: Dimensional Analysis

Chapter 6: Economics

Chapter 7: Problem Solving