Historical Notes for Calculus Teachers

I am in the process of preparing a volume on the above topic. Here are some sections:

• Why the sine has a simple derivative
• Torricelli's Trumpet
• Clepsydra
• History of the Brachistochrone  and How to Build a Brachistochrone.
• The Bridge and the Catenary
• Cauchy's Famous Wrong Proof
  • Documents: Proof in the Cours d'Analyse (1821) is on pp. 131-132. The condensation test is also here.
• Schwarz's Paradox
• L'Hospital's Rule
• Derivative of the sine function

NB. Teachers are encouraged to use this material in the classroom --- but I would very much appreciate feedback about how these could be improved. Send an email to Fred Rickey.