Calculus Projects

Using The Materials

Many of the projects below have data sets associated with them. In those cases curve fitting is used to create a function that models the data so that calculus techniques can be used.  There are now enough version of Excel around that it would be difficult to put directions on curve fitting here for all of them, but here is one for Window Excel 2007. If you have a different version of Excel you basically need to create a scatter plot and then add a trendline (google your version of excel and add trendline). The projects will have a scatter plot with a curve if you don't want to do the curve fitting. If you do just delete the graph and provide students with the data. Each project tile has links to related background information. The materials are posted here to be used and may be used freely and edited as you see fit. The thumbnail graphs in the tiles along with the curve fitting where done with RNew (6/2020) Each tile now has a csv file without metadata of the data used for the graphs. The R files are coded to import these files directly from the website.

Calculus I - Differentiation Related Projects

Mauna Loa Yearly Average CO2

  • Data: Excel File or CSV File (9/2022)
  • Project: Word
  • R Script
  • Skills: Polynomial Differentiation, Tangent Line Problem
  • Note: The Word file contains the graph and the equation. If you would like students to do the curve fitting then delete the graph and give them the excel file.
  • Learn more about CO2 as a greenhouse gas: EPA overview of greenhouse gasses

Global Average Temperature

Global Marine Surface Methane

Arctic Sea Ice

  • Data: Excel File or CSV File (6/2020)
  • Project: Word
  • R Script
  • Skills: Sixth degree polynomial differentiation, max/min, finding roots.
  • Notes: This is an excellent example of a meaningful inflection point. Students will need technology to solve for zero in this project.
  • Learn More about Ice-Albedo Feedback:  The NSIDC has a quick thermodynamics lesson  (five tabs along the top and there are other helpful links on the right - explore them) and  Windows to the Universe.

Country Photovoltaic Energy Production (and more)

  • Data: Excel File or CSV File (6/2020)
  • Note: The Excel file also includes historic production capacity and Solar Electricity Stats.  There is more data in the spreadsheet than used here and there are likely multiple interesting uses of this data.
  • Project: Word
  • R Script
  • The assignment includes three logistic curves (Germany, Italy, and U.S.) and two exponential curves (U.S. and World). The excel file includes more countries that can be used.
  • Skills: Differentiating Logistic and Exponential Functions, Quotient (or Product) Rule,
  • Learn more about solar power as an energy source: Scientific American article, The Age of Wind and Solar Is Closer Than You Think, and one from the Guardian, What is holding back the growth of solar power?

Wind Energy by Selected Countries and World

U.S. Coal Consumption and Production

World Population

  • Data: Excel File or CSV File (6/2020)
  • Project: Word
  • R Script
  • Notes: The main goal of this project is to illustrate the differences of the growth of exponential and quadratic functions. Second to that is the comparisons to U.N. projects are off suggesting they are using a different model. The excel file contains decade population data (used for the project) and yearly population data for those interested.
  • Skills: Polynomial and Exponential Differentiation, Tangent Line Problem.

The Ozone Hole

  • Data: Excel File or CSV File (6/2020)
  • Project: Word
  • R Script
  • Skills: Polynomial Differentiation.
  • Notes: One of the main points of the exercises here is to see the impact of regulations and how we can make changes so that unwanted extrapolations don't happen. This exercise also shows how extrapolations can be far off especially when something changes. The excel file contains more data than used in the assignment.
  • Learn more about the ozone hole: NASA ozone hole watch and NOAA assessment of ozone depletion.

Historical Whale Oil Harvested and Prices

  • Data: Excel File or CSV File (Historic Data from Ugo Bardi - No Updates Needed)
  • Project:  Word
  • R Script
  • Follow up project: Word  This uses the same data as in the first assignment and has students curve fit using a TI-84 calculator (directions included), although consider using R or Excel instead.
  • Notes: The file provided is used as an introduction to curve fitting and, in particular, it demonstrates issues with extrapolation. This is also an opportunity to talk about finite resources and peaking.  The Excel file contains more data than is used in the assignment.  There are notes in the Word file for instructors.
  • Learn more about the history of whale oilnon renewable energy explained from the EIA,  and examples of resources in decline from the World Counts. 

Example Final Paper Based on Some of the Data Here

  • Project:  PDF
  • Note: This is one example on how to bring a number of these together in a final report.

Calculus I - Integration Related Projects

Ecosystem Service - Rain Runoff

U.S. and China CO2 Emissions

World Petroleum Consumption

  • Data: Excel File  or CSV File (6/2020)
  • Project: Word
  • R Script
  • Skills: Setting up and solving and equation with an integral and one with just a function.
  • Notes: Setting up the equations here may not be easy for students. This project also demonstrates the relationship between a function and its integral. The excel file also contains production along with consumption data.
  • Learn more about oil reserves and peak oil: Lengthy but good 2014 paper The future of oil supply by Miller and Sorrell  (figure 7 could be good to discuss in class).

Gini Coefficient Transition to Integration

  • Data: Excel File or CSV File (This data doesn't require updates,)
  • Project:  Word
  • R script
  • Notes: Overall, this assignment moves from differentiation ideas with an application of the mean value theorem to integration. Once students can integrate, you can return to this project and have students find the Gini coefficients. Note that you will need some form of technology to solve higher order polynomial for zero. This project is a really nice way to motive the need for the area under the curve before starting an integration unit.
  • Skills: Mean Value Theorem, polynomial differentiation, and finding the roots of a higher order polynomial.
  • Sustainability Goal: Learn one way inequality is measured.
  • Learn more about the Gini Coefficient: Online paper at NumeracyMeasuring Resource Inequality: The Gini Coefficient
  • Extra Materials: John Stewart talks about the Gini Coefficent This is a 2011 video and shows the ranking of U.S. income inequality by the gini coef as reported by the CIA.

Calculus and/or Differential Equations Projects

Sustainable Fisheries Project