# Tom Morley's 6581

Hello.

Welcome to Mathematics 6581, Winter quarter 1999.

Calculus of Variations

Class is MWF 9 am in ESM 209. 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.

Homework Set Number 2a -- Due Feb 17
• 3.23, 3.26,3.27, 3.29, 3.41(a)
Homework set Number 2b -- Due Feb 24
• (page 186) 6.3,6.4,6.16,6.29

First Homework Set
Due January 27
• Chapter 1, page 31 -- 1.3, 1.7, 1.9
• Chapter 2, page -- 2.2, 2.5 (a), (c), (e), (h), 2.7

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 and here ) 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 Variations is the Irish mathematician William Rowan Hamilton -- see also here. Here is a paper of Hamilton's on the Calculus of Variations.

Help stamp out meaningless symbolic manipulation