# Mathematical Modeling in the Environment

Catalog Code: ENV
Print ISBN: 978-0-88385-709-0
312 pp., Paperbound, 1998
List Price: $65.95 Member Price:$52.95
Series: MAA Textbooks

Suitable for classroom adoption in an innovative course for:

• a general education mathematics elective
• a mathematics or science major advanced elective
• an interdisciplinary course, even at a relatively elementary level
• a mathematical modeling course in a civil/environmental engineering program

This book has a dual objective: first, to introduce the reader to some of the most important and widespread environmental issues of the day; and second, to illustrate the vital role played by mathematical models in investigating these issues. The environmental issues addressed include: ground-water contamination, air pollution, and hazardous material emergencies. These issues are presented in their full real-world context, not as scientific or mathematical abstractions; and for background readers are invited to investigate their presence in their own communities.

The first part of the book leads the reader through relatively elementary modeling of these phenomena, including simple algebraic equations for ground water, slightly more complex algebraic equations (preferably implemented on a spreadsheet or other computerized framework) for air pollution, and a fully computerized modeling package for hazardous materials incident analysis. The interplay between physical intuition and mathematical analysis is emphasized.

The second part of the book returns to the same three subjects but with a higher level of mathematical sophistication (adjustable to the preparation of the reader by selection of subsections.) Many important classical mathematical themes are developed through this context, examples coming from single and multivariable calculus, differential equations, numerical analysis, linear algebra, and probability. The material is presented in such a way as to minimize the required background and to encourage the subsequent study of some of these fields.

An elementary course for a general audience could be based entirely on Part I, and a higher level mathematics, science, or engineering course could move quickly to Part 2. The exercises in both parts tend to be quite thought-provoking and considerable course time might be well devoted to discussing their solutions, perhaps even in a seminar format. The emphasis throughout is on fundamental principles and concepts, not on achieving technical mastery of state-of-the-art-models.

Dedication
Preface
Acknowledgements
Part 1: An Interdisciplinary Introduction to Selected Problems in Ground Water, Air Pollution, and Hazardous Materials
Chapter 1: Introduction
Chapter 2: Ground Water
Chapter 3: Air Quality Modeling
Chapter 4: Hazardous Materials Management
Part 2: Further Development of Modeling Concepts
Chapter 5: Additional Topics in Ground Water
Chapter 6: Additional Topics in Air Modeling and Diffusion Processes
Chapter 7: Additional Topics in Hazardous Materials Modeling
Index

### Excerpt: 2.4 Darcy's Law (p. 19)

In developing any kind of mathematical model, you need to figure out what the key physical variables are that control the situation of interest. We are interested here in the flow of ground water through some kind of porous geologic medium. In about 1850 a French engineer named Henri Darcy was interested in essentially the same question because he was trying to set up a system for filtering water in the city of Dijon, France, by passing it through beds of clean sand (such sand filters are still commonly used today.) The question he faced was really how much water could move at what rate through what size sand filter. To answer this question, he set up some simple experiements.