Description
Following in the tradition of Consider a Spherical Cow, the Cylindrical Cow will help students achieve a whole new level of environmental modeling and problem solving. Featuring a new core set of 25 fully worked-out problems, this book uses real problems in environmental science rather than relying on the more traditional “cookbook” problems found in textbooks. It is organized according to five thematic sections on probability, optimization, scaling, differential equations, and stability and feedback. Each section begins with a general treatment of the relevant mathematical concepts, and concludes with a range of homework exercises to help students sharpen their modeling skills. Like its predecessor, this book will empower students with the mathematical skills needed to cut through the complexity of real-world problems.
Chapter I PROBABILITY
Introduction
Background
Problems
1. Pick Your Poison
2. Infanticide in China?
3. Caesar's Last Breath
4. A blot from the Blue?
5. On the Street Where You Live
Chapter II OPTIMIZATION
Introduction
Background
Problems
1. Advice for Farmers
2. Efficient Censusing
3. Blowing in the Wind
4. Haste Makes Waste
5. Biting the Hand that Feeds Us
Chapter III SCALING AND DIMENSIONAL CONSISTENCY
Introduction
Background
Problems
1. How Tall Can a Mountain Be?
2. Sleeping Bears
3. Little Green Men?
4. What a Drag
5. Saving the Species: The role of Reserve Shape
Chapter IV CORE MODELS OF CHANGE IN TIME AND SPACE
Introduction
Background
Problems
1. Pollutant Stock-and-Flow: Reconstructing CO2 Emissions
2. Population: Limits to Growth
3. Climate: Influence of Solar Variability
4. Community Ecology: Origins of Cycles
5. Biogeochemistry: Nitrogen Fertilization and the Carbon Sink
Chapter V STABILITY AND FEEDBACK
Introduction
Background
Problems
1. Stability of the Core Models
2. Some Say in Ice
3. Biting the Hand that Feeds Us (II)
4. Sagebrush World
5. Will the Seas Go Flat?
Appendix: Useful Mathematical Expressions and Approximations
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