The Impact of Mathematics on Society

Explore the diverse applications of mathematics in society, from economic growth to energy consumption trends. Discover how calculus influences our understanding of economics and oil production dynamics, shaping critical decisions for the future. Uncover the essential role of mathematics in analyzing and maintaining a thriving economy and sustainable energy practices. Delve into the intricate relationships modeled by mathematical formulas to forecast trends and inform policymaking. Witness the profound influence of mathematics on shaping the world we live in.

• Mathematics
• Society
• Economics
• Calculus
• Energy

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Uploaded on Feb 28, 2025 | 0 Views

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1. Pronken met andermans veren Wat heb je aan wiskunde? Wat heeft de maatschappij aan wiskunde? Powered by

2. Calculus: Affecting the Lives of Millions Deborah Hughes Hallett Department of Mathematics, University of Arizona Kennedy School of Government, Harvard University Hands on TI-Nspire Session: Ann Davidian, MacArthur HS, Levittown, NY Powered by

3. What Does it Take to Maintain Our Economy? http://en.wikipedia.org/wiki/Economy_of_the_United_States February 21, 2012: Wall Street Journal Fannie Mae Sees 2012 US Economy Growth Of 2.3%, Up From 1.6% In 2011 Feb. 26, 2012: Bloomberg Businessweek Manufacturing probably accelerated for a fourth straight month in February, consumer confidence improved and Americans picked up the pace of spending a month earlier .. Powered by

4. US GDP per capita If the economy is shrinking, we have a recession If the economy is not changing, it is stagnant What does it take to keep the economy expanding? Powered by

5. An Expanding Economy Requires More Energy How long can we increase energy consumption each year? It depends partly on the source: Supply of oil is finite What is peak oil production? When will/did US oil production peak? When will/did world oil production peak? Based on Calculus, Hughes Hallett at al, 2009. Uses data at http://cta.ornl.gov/data/chapter1.shtml http://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=5&pid=53&aid=1 Powered by

6. What Mathematics Models US Oil Production? Let P be the total quantity of oil produced in the US since 1859, when the first oil well was built; P is in billions of barrels. Let t be time in years Then dP/dt is approximately US annual oil production What is the relationship governing changes in P? Powered by

7. Look at Relative Growth Rate: (dP/dt)/P Exponential growth: (dP/dt)/P is constant Can t hold for long; P would increase indefinitely Logistic growth: (dP/dt)/P is linearly decreasing function of P or Powered by

8. What are k and L? What does k represent? Exponential growth rate for small P What does L represent? Value of P for which dP/dt is zero Total US oil reserves How do we estimate k and L? (dP/dt)/P is linear function of P; use scatter plot and linear regression Powered by

9. History: M. King Hubbert In 1956, the US geologist Hubbert gave a paper in San Antonio analyzing US oil production and predicting peak oil. Using data he would have had gives us: US Oil Production 1931-1950 0.07 0.06 0.05 (1/P)dP/dt 0.04 y = -0.00036x + 0.0649 0.03 0.02 0.01 0 0 5 10 15 20 25 30 35 40 45 P, total production (bn barrels) Powered by

10. Differential Equation and Solution We get k = 0.0649 and L = 180 billion barrels So the differential equation is: With t = 0 in 1950, and P0= 40.9, its solution is the logistic function: Powered by

11. How Do We Find When Peak Oil Occurs? L A logistic curve has the shape shown: L/2 Where is L? Where is maximum rate? http://www.jmu.edu/geology/ComplexEvolutionarySystems/ChaosTheory.htm Peak Oil occurs when P = L/2 Powered by

12. For Hubberts Model Set the denominator to 2 and solve for t, giving t 19. Since we took t = 0 in 1950, Hubbert s prediction was 1969. (In fact, he said 1965-70). What happened about that time? A few years later? Powered by

13. http://www.heatingoil.com/articles/arab-oil-embargo-happened-happen/http://www.heatingoil.com/articles/arab-oil-embargo-happened-happen/ http://www.saskschools.ca/curr_content/socst10_05/images/oil_crisis.jpg Politics played a role too Later foreign oil imports grew 1970 s Oil Crisis Gas lines, Brooklyn 1973 http://artnectar.com/2010/02/1970s-new-york-city-in-pictures/ Powered by

14. Annual US Oil Production, 1900-2010 US Oil Production dP/dt vs. P: Model predicts Quadratic 4 3.5 3 dP/dt (billions of barrels per year) 2.5 2 y = -0.0002x2+ 0.0543x + 0.1534 R = 0.9844 1.5 1 0.5 0 0 50 100 150 200 250 P (billions of barrels) Powered by

15. Total US Oil Production, 1900-2010 US Oil Total Production since 1859 P vs. t: Model Predicts Logistic 250 P, Total production in billions of barrels 200 150 100 50 0 0 20 40 60 80 100 120 Years since 1900 Powered by

16. What is the Calculus Involved in Predicting Peak Oil? Initial value problem Solving differential equation using integration Estimating asymptotes and point of maximum slope Exponentials and logarithms Regression (involves optimization) Linear, quadratic, and logistic functions Powered by

17. When is World Oil Predicted to Peak? Production: All liquid Fossil Fuels, bn barrels per year http://planetforlife.com/oilcrisis/oilpeak.html http://en.wikipedia.org/wiki/Peak_oil Powered by

18. Commemorating Hubberts Willingness to Announce What He Saw in the Mathematics http://www.mkinghubbert.com/ and http://www.thecuttingedgenews.com/index.php?article=476 In 1950, the United States was largely self sufficient on oil. It was the world s largest producer and exporter of oil. She had just emerged relatively unscathed from of the second of two world wars for which her unprecedented access to oil proved the deciding factor. ...The sun was rising on America . In this context of American exuberance and seeming mastery of the world, M. King Hubbert took a stand .. forecasting that the ultimate source of American power oil Texas gold was headed for imminent decline and he did it in the heart of the oil patch. "Our ignorance is not so vast as our failure to use what we know. M. King Hubbert Powered by

19. Mathematics can be used to improve the lives of millions, all over the world Powered by