# Math 5403 (Calculus of Variations)

# Fall 2004

** Instructor: **

John Albert Office: PHSC 1004, Ext.
5-3782. Office hours: Mon, 10:30 AM; Wed and Thurs, 2:30-3:30
PM (or by appointment) E-mail: jalbert@ou.edu

Here is the syllabus for this course.
NOTE 1: There is a mistake in the expression for the second-order
Taylor expansion for functions of two variables in the notes I handed out in the final week
of class. There is a "2" missing in front of the mixed derivative term (the second partial
derivative of f with respect to first x and then y). An example of the correct formula,
with the 2 where it belongs, is in equation (6) on p. 101 of the text.
NOTE 2: I promised in class that I would put up a solution to some of the problems
on Assignment 7. As of now (Sunday night) I've only written up one solution, to
problem 10 on p. 130. The tricky part of this problem was to locate the conjugate points
for the extremals. Actually, you do not need to worry about conjugate points for the
exam, as I have already written the exam and have put no questions about conjugate points
on it. But reading the solution to this problem may help you to mentally organize what you know about necessary and/or sufficient conditions
for local minima.
NOTE 3: I also hoped I would put something up on this web page which finishes the unfinished lecture I gave
on the last day of class, and shows which of the two extremals for the hanging cable problem is
the local minimum. I haven't put that up yet, but I will eventually. So if you still want to see how
that works out, check back here in a few days.
NOTE 4: As of summer 2005, I still haven't got around to posting the rest of the unfinished lecture.
Anybody who wants to see it might be better off coming to my office where I will gladly scrawl it on
the blackboard.