The book was written on the assumption that you have learned introductory algebra and that you have learned how to combine units of measurement. It is useful to refresh your memory in these areas at the outset. Appendix A reminds you how units are defined and combined. Appendix B describes exponential growth and decay, two of the more important topics from your previous study of mathematics

You do not need to know calculus or differential equations to use this book. Rather, you'll learn how to build mathematical models on the computer. Your job is to concentrate on the structure of the model; the tedious job of numerical simulation will be left to the computer.

Computer simulation is made easier by software such as Stella (Appendix C), Dynamo (Appendix D), Vensim (Appendix E), and Powersim (Appendix F). Stella is used in this book, so you will find the most direct match between your work and the book if you use Stella. However, you can use any of the software packages with this book. Each is easy to learn, and each can be used to build powerful models of environmental systems.
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Material flows are of special interest to environmental scientists and managers, and system dynamics is well suited to simulate material flows because of the clarity of the stock and flow approach. Chapter 10 describes the methods most frequently used to simulate material flows through a system. Chapter 11 draws our attention to the fast moving flows and explains how they influence the selection of DT, the 'step size' in numerical simulations.

The book then presents three applications to real environmental systems. Chapter 12 describes the flow of the pesticide DDT through the soil, the air, and the ocean and into the bodies of fish. Chapter 13 describes the salmon smolts' spring migration down the Snake River, down the Columbia River and into the ocean. Chapter 14 describes the life cycle of the salmon born in the Tucannon River in eastern Washington.
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Chapter 15 describes the process of building and testing a model. This is a trial and error process involving a combination of all the skills learned from the previous chapters. You'll read that experienced modelers concentrate as much on the process of model building as the model itself. Chapter 15 concludes with cases in which the iterative nature of the modeling process was the key to project success.

Chapter 16 demonstrates the iterative process of modeling with a concrete example of the deer herd on the Kaibab Plateau in northern Arizona. After several iterations, chapter 16 arrives at a model to explain the rapid growth and subsequent collapse of the deer herd in the 1920s. The Kaibab example is a vivid illustration of the 'overshoot' pattern of behavior that may be observed in a wide variety of systems.
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The next three chapters turn our attention from systems that grow over time to systems that oscillate over time. The oscillations may be extremely volatile and pose serious problems, or they may be highly stable and provide the key to the system's longevity. Chapter 17 explains the fundamentals of oscillatory by drawing on the examples of S shaped growth from chapter 6. You'll read how the introduction of delays can change the stable systems from the previous chapter into highly oscillatory systems.

Two examples are provided to allow you to build and test models of oscillatory behavior. The first example is predator-prey cycles, one of the most widely discussed topics from ecology. Chapter 18 describes cyclical patterns in a population of cougars and deer on the Kaibab Plateau. The second example is commodity production cycles, one of the more important topics from economics. Chapter 19 describes a model of production cycles in the world aluminum industry.
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The next two chapters are devoted to management flight simulators. These are highly interactive models designed for ease of experimentation. The first example deals with the persistent problem of urban air pollution. Chapter 20 places you in the role of 'feebate manager.' By charging fees on the sale of dirty vehicles and allowing rebates for the purchase of clean vehicles, a state might reduce vehicle emissions within the urban air shed. Chapter 20 challenges you to learn whether a feebate program could be designed to operate in a financially prudent manner.

The second example deals with the Gaia Hypothesis and the parable of daisyworld. Chapter 21 provides a brief review of the Gaia Hypothesis and the purpose of the mathematical model of an imaginary planet with black and white daisies. You'll use the flight simulator to design a world with the best possible prospects for sustaining life on daisyworld.
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The two concluding chapters deal with the topics of validation and model use. Chapter 22 introduces opposing points of view on the controversial topic of model validation. It adopts a pragmatic point of view and explains five concrete tests that can be used to bolster confidence in a model.

Of course, the ultimate test of a model's usefulness if whether it is put to use. System dynamics models have been put to extensive use in the electric power industry. Chapter 23 reviews the history of this industry, and it describes how system dynamics has contributed a unique perspective on the industry's problems. The lessons from this industry will help you anticipate how the knowledge from this book might be used in your own field.
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The appendices provide important material that is not normally read in sequential fashion. You should pick and choose which appendices will best support your own learning. The first two appendices are review material. Almost every reader will benefit from a quick review of units (Appendix A) and mathematics (Appendix B).

The next six appendices deal with software. Stella is described in detail in Appendix C because it has been selected for the examples in the book. But you will quickly see the close similarity between Stella and the other stock and flow programs by reading appendices D, E and F.

If you are familiar with spreadsheets, you will benefit from the description of spreadsheet modeling in Appendix G. Appendix H concludes the software material with an introduction to some of the special functions that expand the power of models beyond the normal stocks and flows.

The final three appendices cover special topics of interest to students of the environment. Environmental scientists and managers often pay close attention to spatial arrangements, and Appendix I illustrates how the spatial dimensions can be included in a system dynamics model. The illustration shows the spread of nitrogen in a catchment.

Appendix J is of special interest to environmental managers using models with many, highly uncertain parameters. It explains how we may calculate the confidence bounds for model simulations. It then illustrates how the feedback structure of a system causes the confidence bounds to grow or shrink over time.

Appendix K concludes with the Idagon, a management flight simulator that allows you to experience the challenges of managing a complex river system. You'll see a summary of the river system in the appendix. The detailed description and the flight simulator are on this home page.
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