Tom Pfaff's Sustainability Page

Calculus Materials

  • The main idea for most of the calculus material 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. Please contact me about if you have any questions, suggestions, or comments: tpfaff(at)
  • 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 (6/11) Tex
Function Composition, Polynomial Differentiation, Tangent Line Problem
Atmospheric Methane (New 9/11) (N/A for now) The curve fitting here is logarithmic.
US Coal Consumption (6/11) Tex
Linear Differentiation, Solving Equations
World Grain Balance (6/11) Tex
(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 (6/11) Tex
Polynomial Differentiation, Integration
World Population (9/11) Tex
Polynomial and Exponential Differentiation, Tangent Line Problem
World and by Country Photovoltaic Energy Production (9/11) Tex
Polynomial/Exponential Differentiation, Quotient (or Product) Rule
Wind Energy by Selected Countries and World (9/11) Tex
Polynomial/Exponential Differentiation, Quotient (or Product) Rule
U.S. and China CO2 emissions (9/11) Tex
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
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 (9/11) 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.

Created by Thomas J. Pfaff and last updated on 09/19/11. Send questions or comments to tpfaff(at)