Tom Pfaff's Sustainability Page
Are you concerned about the State of the Planet? Do you wish you could help? Why not bring a sustainability theme to your calculus classes? It's easy and rewarding and can be incorporated into the class without changing the typical calculus content.

As one student commented anonymously "...for once a math class used real world information for their questions/problems instead of just pulling numbers out of nowhere and expecting we understand them ."

On this page you will find data sets, example worksheets, and the background information you need to incorporate a sustainability theme into your Calculus I course (feel free to use anything here for other courses as well). There are also links for further reading for you or your students.

The basic idea is simple: students use Excel to fit curves/functions to real data (using at most one day of class time) on global average temperature, grain consumption, atmospheric CO2, etc. (simple instructions for curve fitting in Excel are also provided). Once we have the functions, calculus tools can be used to answer important sustainability questions.

If you are finding this page useful in any way (especially if you are using any of this in a class), if you have a comment for improving this page, or want help incorporating sustainability into a calculus class please send me an email: tpfaff(at)ithaca.edu

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  • Are you not sure what sustainability means or know others that don't seem to understand? Well this might help: Top Ten Myths About Sustainability by Scientific American.
  • The table below contains individual data sets in an Excel sheet (with citations for data), related assignments, and calcuus skills used in the assignments. The assignments do not use all the data that is available and hence there is plenty of opportunity to develop other assignments. Also, the all data file includes other data sets than those listed separately and may be more up to date than the individual files. Here is a one page set of instructions for curve fitting with Excel: EXCEL CURVE FITTING INSTRUCTIONS: Excel 1997- 2003 or EXCEL CURVE FITTING INSTRUCTIONS: Excel 2007

DATA-xls (checked for update) Assignments Calculus/Math Skills
Atmosphere: CO2 & Temp (8/09) Tex
Word 		Function Composition, Polynomial Differentiation, Tangent Line Problem
US Coal Consumption (8/09) Tex
Word 		Linear Differentiation, Solving Equations
World Grain Balance (8/09)

World Grain Balance Old (N/A)

Tex
Word 		(Note: The data set is much more robust now, Grain Old is the previous file if you would prefer that.) Polynomial Differentiation, Create Tangent Line and Solve, Max/Min
World Oil Consumption (8/09) Tex
Word 		Polynomial Differentiation, Integration
World Population (8/09) Tex
Word 		Polynomial and Exponential Differentiation, Tangent Line Problem
World and by Country Photovoltaic Energy Production (8/09) Tex
Word 		Polynomial/Exponential Differentiation, Quotient (or Product) Rule
Wind Energy by Selected Countries and World (8/09) Tex
Word 		Polynomial/Exponential Differentiation, Quotient (or Product) Rule
U.S. and China CO2 emissions (9/09) Tex
Word 		Polynomial Differentiation and Integration
US Vehicles: counts & miles traveled (11/08) None This data can be used for a more advanced modeling projects to study the effect of increased CAFE standards, which could include max/min problems.
Ozone Hole (12/07) Tex
Word 		Polynomial Differentiation. Note: The main point of the exercises here is to see the impact of regulations and how we can make changes so that unwanted extrapolations don't happen.
ALL DATA (11/08) Instruction for a final Paper based on assignments above As Above
Historical Whale Oil Harvested and Prices This data is due to Prof Ugo Bardi and there is a citation in the spreadsheet to a related paper. Tex
The file provided is used as an introduction to curve fitting and provides an opportunity to talk about finite resources and peaking. There are notes in the tex file for instructors.

  • This table is similar to the one above. The only difference here is the material is contributed by other people. If you would like to add something to this table go ahead and send me an email.

DATA-xls (updated) Assignments Contributor
U.S. and World Energy Consumption (7/16) Word Contributed by Naomi Hamermesh a student from Bryn Mawr College.

  • Resources for Statistics (this is more of a work in prograss than the above table for caclus so if you have comments or suggestions please let me know).
DATA-xls (updated) Assignments Statistics/Math Skills
U.S. Oil Consumption (11/08) pdf The excel file contains U.S. Oil extraction data and is set up to use goal sit to do a normal model least squares curve fit. In the pdf file studenst do basic normal probabilyt type questions about the U.S. oil model. The Excel sheet itself is interesting as it is set up to fit the data knowing only what Hubbert knew (I think) as long as all the current data. One can change the total oil extracted value to see how the peak and fit doesn't change much.
Global Temperature Anomolies, Relative to 1961-1990, 1850-present (6/09) pdf This is a regrssion exercise to reproduce the graphic found here and used in many places.
  • Useful resources for further activity development or class use.
    • Saudi Arabia Peak Oil The first graph in this article is loaded with information and well done. The article is about the possibility that Saudi Arabia oil production is in decline and has business and economic themes throughout.
Created by Thomas J. Pfaff and last updated on 8/6/09. Send questions or comments to tpfaff(at)ithaca.edu. HOME Large Black on White Ithaca Logo