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### EarthCalculus

###### Resources and Worksheets for Adventurous Instructors

Kaisa Taipale

I am a mathematician who loves contemplating the purest of the pure (string theory is so cool!) and the messiest of the messy (what's the mathematics of composting?). Contemplation is not enough, though. I like to make stuff! Hence the book.

EarthCalculus is a book about the calculus on Planet Earth, beyond gravitation. My students are interested in the environment, nature, the planet, and our interactions with it -- and calculus has tools to deal with the messy problems of groundwater usage, optimization of fertilizer use, and many other surprisingly subtle problems. It's so much more fun to demonstrate the open-ended powers and pitfalls of mathematics than just do problems from standard texts. EarthCalculus aims to give profs and students quick introductions to those interesting real-life problems, with dozens of in-class worksheets to get students' hands messy.

• Introduction
• Approaching calculus through an earth-lens
• Precalculus worksheets
• Lines: A linear beginning
• Composition of functions: group work and a power function for atmospheric pressure
• Trigonometric functions: lynx!
• Reading graphs: nitrates in the Raccoon River
• Limits and continuity: drugs in our waterways
• Inverse functions: revisiting the mountains
• Volume and area: White Bear Lake
• Increasing and decreasing: nitrates in the Raccoon River
• Using short projects
• Incorporating short projects
• Spreadsheets in the calculus classroom: Point Reyes tidal data
• Differentiation
• Rate of change: aquifers and groundwater
• Rate of change: White Bear Lake surface level
• Rates of rates of change: atmospheric pressure in mountains
• Graphing: the mathematical stories
• The chain rule: a better model for lynx populations
• Inverses and derivatives: more altitude problems
• Derivatives mix: drugs in our waterways
• Optimization: give me some optimal sugar!
• Related rates: compost oh compost
• Derivation of equation for atmospheric pressure
• Integration and differential equations
• Numerical integration: drinking drugs in Denver
• Differential equations: our leaky atmosphere
• Sea ice: a very baby model
• Further resources
• Other calc resources

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