Math 727: Calculus of Variations

Prerequisites:

Prerequisites: Ordinary Differential Equations (Math 319), Undergraduate Analysis (Math 521) or equivalent. Math 721 is not a prerequisite, but it will be very helpful.

Instructor:

Sergey Bolotin

Time and Place:

MWF 13:20-14:10

textbooks:

Possible text: G. Buttazzo, M. Giaquinta, S. Hildebrandt, One-dimensional Variational Problems, Oxford Lecture Series in Mathematics, Vol. 15, OUP (1998).

Course Content:

Calculus of variations is one of the oldest mathematical subjects but still an active field of research. This course is mainly about one dimensional calculus of variations where no serious functional analysis is required. We will start with necessary conditions for an extremum, Euler-Lagrange equations, theory of second variation, and then proceed to sufficient conditions and field theory. In the second part of the course we develop direct methods of the calculus of variations and prove existence theorems for minima and other types of critical points. This requires some basic tools from functional analysis. Applications will be chosen from geometry, differential equations and classical mechanics.