Calculus of Variations, Summer 2001

Tom Morley's Calculus of Variations

Hello.

Welcome to MathematicsCalculus of Variations, Summer quarter 1998.



Final Exam:

• Page 227: 7.14, 7.16
• page 372: 10.1, 10.5

Class is MWF 8 am in Space Science LH III. The textbook is John L. Troutman,
Variational Calculus and Optimal Control . We will start by covering chapters 1 through 6, and then see where we are, and what the class interests are.

The grade will be based on a series of Homework assigments (70%), and the final (30%),
which will be open book and notes. If there is time, we may have a (computer project) which will count in the homework.

A fine book which we will ocasionally refer to is Goldstein's Classical Mechanics , although no prerequisite of physics will be assumed.

There is also a great introduction to Calculus of Variations in
Chapter 21 of Vol II of Feynmann's Lectures on Physics.

Calculus of Variations was first invented by Johann Bernoulli , (see also here andhere ) when he challanged mathematicians to find the brachistochrone. His solution was by analogy with optics. (See book page31 Exercise 1.1). Other solutions were obtained by Jakob Bernoulli (Johann's brother), Newton, Euler, Leibniz, and I belive Daniel Bernoulli.
It is complicated to keep track of all the Bernoulli's --here is the

Family Tree

Another real character that is very important in the Calculus of Variationsis the Irish mathematician
William Rowan Hamilton -- see alsohere.

Here is a A site with Hamilton's papers.