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Extreme Calculus

Extreme Calculus. Paul Zorn Saint Olaf College and MAA. MAA. Math. Assoc. of America. founded 1915 about 25,000 members worldwide focused on college-level math publications meetings professional development, outreach advocacy for mathematics

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Extreme Calculus

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  1. Extreme Calculus Paul Zorn Saint Olaf College and MAA

  2. MAA KC Tech Expo

  3. Math. Assoc. of America • founded 1915 • about 25,000 members worldwide • focused on college-level math • publications • meetings • professional development, outreach • advocacy for mathematics • last 3 presidents from Minnesota … this has to stop KC Tech Expo

  4. MAA headquarters, Washington DC • 1529 18th St NW • built 1903 • residence of Charles Evans Hughes, later Chief Justice of US Supreme Court, Secretary of State in Harding administration, unsuccessful Presidential candidate KC Tech Expo

  5. Founded in Missouri Benjamin Franklin Finkel, Kidder Institute, 1894 KC Tech Expo

  6. Extreme story problems Problem 4, AMM Vol 1. No.1, 1894 KC Tech Expo

  7. Extreme story problems 2 AI = length of one board; GO = “radius” KC Tech Expo

  8. Extreme story problems 3 Answer: area = 196,020 acres (approx) … more than 300 square miles KC Tech Expo

  9. Extreme extremization 4 Problem: Maximize ab subject to a+b=constant Maximize abc subject to a+b+c=constant Answer: a=b or a=b=c or … . Reason: AM-GM inequality: KC Tech Expo

  10. Extreme extremization 5 Problem: Maximize xyz subject to xy + 2xz + 2yz = constant Question: Why would we do this? Guesses? KC Tech Expo

  11. Extreme extremization 5’ Problem: Maximize xyz subject to xy + 2xz + 2yz = constant Answer: xy*2xz*2yz = 4xxyyzz; it’s largest when xy = 2xz = 2yz , so x=y=2z KC Tech Expo

  12. Extreme extremization 5’’ Problem: Maximize subject to Why? Guesses? KC Tech Expo

  13. Extreme extremization 5’’’ Answer: Maximize subject to (instead) Thus KC Tech Expo

  14. Extreme extremization 6 Problem: Find “pie-shaped” region with largest area and total fence-length 100. r * theta r theta r Length = 2r+r*theta = 100 Area= r^2 * theta / 2 KC Tech Expo

  15. Extreme numerics … the harmonic series KC Tech Expo

  16. Extreme blends How does f(x) = x + sin(x) behave? What about f(x) = x + a sin(x) ? f(x) = x + sin(a x) ? KC Tech Expo

  17. Extreme Newton February 1998 June 14 KC Tech Expo

  18. Cubic polynomials … anything new to say? All cubics through these points have same integral as the quadratic June 14 KC Tech Expo

  19. Newton’s method on cubics … some surprises June 14 KC Tech Expo Extreme Calculus

  20. Extreme e June 14 20 KC Tech Expo Extreme Calculus

  21. Definite integrals 6/10/2014 KC Tech Expo Extreme Calculus

  22. How big are these numbers? 6/10/2014 KC Tech Expo Extreme Calculus

  23. Approximating e 6/10/2014 KC Tech Expo Extreme Calculus

  24. Might e be rational? 6/10/2014 KC Tech Expo

  25. On a Rolle -- Gauss/Lucas June 14 KC Tech Expo

  26. Juan Sanchez de Cotan 1603 KC Tech Expo

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