HW05
Assigned:       THU 24 SEP 09
Due:                THU 08 OCT 09

Problem 1.   Boas Problem #1, Ch.11.5, page 542.

Problem 2.   Boas Problem #2, Ch.11.5, page 542.

Problem 3.   Boas Problem #4, Ch.11.5, page 542.

Problem 4.   Boas Problem #6, Ch.11.7, page 544.

Problem 5.   Boas Problem #7, Ch.11.7, page 544.

Problem 6.   Boas Problem #3, Ch.11.8, page 546.

This last problem is the solution to the infamous "Brachistochrone Problem" that led to the invention of the Calculus of Variations. From Wikipedia: "Johann Bernoulli solved the problem ... before posing it to readers of Acta Eruditorum in June 1696. Five mathematicians responded with solutions: Isaac Newton, Jakob Bernoulli (Johann's brother), Gottfried Leibniz, Ehrenfried Walther von Tschirnhaus, and Guillaume de l'Hôpital. Four of the solutions (excluding l'Hôpital's) were published in the May 1697 edition of the same publication."  Newton, who was semi-retired from mathematics and just taking up a position at the Royal Mint of England,  submitted his solution anonymously. Johann Bernoulli immediately recognized that this short and elegant solution — inventing along the way the calculus of variations as a lemma — could only be that of Newton, and exclaimed to his brother, "The Old Lion has again shown his claws!" (Men of Mathematics by E. T. Bell.)



Johann Bernoulli