### 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 R. **New Summer 2018** The .R files that were used to create the graphs have been added to each tile.

### Calculus I - Differentiation Related Projects

### Mauna Loa Yearly Average CO2

- Data: Excel File (6/18)
- 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: Princeton Geosciences and the EPA overview of greenhouse gasses

### Global Average Temperature

- Data: Excel File (6/18)
- Project: Word
- R Script
- Skills: Function Composition, 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 the impacts of climate change: Union of Concerned Scientist Global Warming Impacts or the EPA Student's Guide to Global Climate Change which includes a short video.

### Mauna Loa Yearly Average MH4

- Data: Excel File (6/18)
- Project: Word
- R Script
- Skills: Polynomial Differentiation, Tangent Line Problem.
- Learn More about methane: EPA Methane Emissions, NOAA Trends in Methane, and The NOAA Annual Greenhouse Gas Index (AGGI) (includes information on radiative forcing)
- Feedback loops related to methane: Methane Bubbles and Melting Permafrost

### Arctic Sea Ice

- Data: Excel File (6/18)
- 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 (6/18)
- Note: The data now also includes historic production capacity and Solar Electricity Stats. There is more data in the speadsheet than used here and there are likely multiple interesting uses of this data.
- Project: Word
- R Script
- The assignment includes two logistic curves (Germany and Italy) 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

- Data: Excel File (6/18)
- Note: The excel file includes total installed wind power for selected countries and the world (used in the assignment here) since 1980 and the percent of electricity generated by wind for selected countries since 2010.
- Project: Word
- R Script
- Skills: Polynomial and logistic Differentiation, Quotient (or Product) Rule.
- Learn more about wind power: Wind energy basics from the Department of Energy and the environmental impacts of wind power by the Union of Concerned Scientists.

### U.S. Coal Consumption and Production

- Data: Excel File (6/18)
- Project: Word
- R Script
- Skills: Fourth/fifth degree polynomial differentiation, max, finding roots.
- Notes: Students will need technology to solve for zero in this project. The excel file contains more data than is used here. The project uses production and consumption data but the file also contains coal imports and exports in terms of tons and BTU.
- Learn more about coal: NYT article Coal Production Plummets to Lowest Level in 35 Years and the Economist Peak coal: US coal-fired power is steadily declining

### World Population

- Data: Excel File (6/18)
- 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 census bueraue 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 (7/18)
- 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 (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 oil, non 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

- Data: Excel File (Historic Data from the Hubbard Brook Ecosystem Study - No Updates Needed)
- Project: Word
- R Script
- Skills: Riemann Sums.
- Sustainability Goal: Understand the ecosystem service provided by trees and shrubs in absorbing water runoff.
- Learn more about ecosystem service from the Food and Agricultural Organization (FAO) of the United Nations Ecosystem Services & Biodiversity (ESB) pages.

### U.S. and China CO2 Emissions

- Data: Excel File (7/18)
- Project: Word
- R Script
- Skills: Riemann sums.
- Notes: The use of Riemann sums is basic, but the overall assignment is rich in context and demonstrates the value of area under a curve. The excel file includes total emissions, population, and per capita emissions.
- Learn more about U.S. and China CO2 emissions: Union of Concerned Scientist - Each Country's Share of CO2 Emissions and The World Resource Institute - 6 Graphs Explain the World’s Top 10 Emitters

### World Petroleum Consumption

- Data: Excel File (7/18)
- 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 (7/18 - this data doesn't need regular 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 Numeracy: Measuring 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

- Project: Word
- Notes: This assignment references a NOAA report (see Estimation & Projection Methodology) on fisheries and sustainable harvest.
- Skills: Slope fields and separable equations.
- Sustainability Goals: Understanding the challenges of sustaining fisheries.
- Learn more about global fish stock: 2012 BBC article, World Ocean Review, 2016 FAO Report (The state of fisheries starts on page 38.)