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Augustin-Louis Cauchy and Derivatives

Augustin-Louis Cauchy and Derivatives. Warm-Up. Motivation. Business – gain or loss in profit Cars – figure out speed at a certain point Health – growth in height over a period of time. History. Born in Paris in 1789 Received early education from his father

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Augustin-Louis Cauchy and Derivatives

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  1. Augustin-Louis Cauchy and Derivatives

  2. Warm-Up

  3. Motivation Business – gain or loss in profit Cars – figure out speed at a certain point Health – growth in height over a period of time

  4. History Born in Paris in 1789 Received early education from his father He initially prepared himself to be a civil engineer He entered the ĒcolePolytechnique in 1805, where he met Lagrange and Laplace who later persuaded him to study pure science.

  5. Teachings He was a professor at Ēcole Polytechnique His main job was teaching calculus and he was not satisfied with the way the foundations of the subject then stood. His goal was to “do calculus right” The result was one of the most famous textbooks in the history of mathematics, The Ēcole Polytechnique Course in Analysis.

  6. Works • He can be ranked next to Euler in volume of output • He wrote extensively in both pure and applied math • several books • 789 papers, some of which are very extensive works • Cauchy wrote such lengthy articles the Academy of Sciences quickly passed a rule limiting all papers to a maximum of four pages because the printing bill was high.

  7. Contributions • Cauchy gave numerous contributions to advanced mathematics • researches in convergence and divergence of infinite series • real and complex function theory • differential equations • determinants • probability • mathematical physics

  8. Contributions to Calculus Cauchy root test and Cauchy ratio test for convergence and divergence Cauchy product of two given series Basic concepts of limits and continuity Definition of derivative He used the notion of a limit as the basis for a rigorous foundation for calculus

  9. The Derivative

  10. Definition of Derivative

  11. http://www.clas.ucsb.edu/staff/lee/secant,%20tangent,%20and%20derivatives.htmhttp://www.clas.ucsb.edu/staff/lee/secant,%20tangent,%20and%20derivatives.htm

  12. Steps Replace x with x+h Simplify numerator Factor h out of numerator Divide by h Plug in 0 for h Evaluate slope

  13. Example 1

  14. Pascal’s Triangle

  15. Find a buddy!

  16. Practice

  17. Answers

  18. Recap

  19. Independent Practice • Homework: • Pg. 324 #’s 1, 3, 6, 7, 11, 13, 17

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