Augustin-Louis Cauchy and Derivatives
Warm-Up
Business – gain or loss in profit
Cars – figure out speed at a certain point
Health – growth in height over a period of time
Motivation
Born in Paris in 1789
Received early education from his father
He initially prepared himself to be a civil engineer
He entered the Ēcole Polytechnique in 1805, where he met Lagrange and Laplace who later persuaded him to study pure science.
History
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.
Teachings
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.
Works
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
Contributions
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
Contributions to Calculus
The Derivative
Definition of Derivative
http://www.clas.ucsb.edu/staff/lee/secant,%20tangent,%20and%20derivatives.htm
1. Replace x with x+h2. Simplify numerator3. Factor h out of numerator4. Divide by h5. Plug in 0 for h6. Evaluate slope
Steps
Example 1
Pascal’s Triangle
Find a buddy!
Practice
Answers
Recap
Homework: Pg. 324 #’s 1, 3, 6, 7, 11, 13, 17
Independent Practice