Time and place:

Lectures: MWF 2:00-2:50, Thack 525

Instructor: Anna Vainchtein

Office Hours: W 11-12 am and 1-2 pm, or by appointment (send me an e-mail)
Office: Thackeray 611
Phone: (412) 624-8309
E-mail: aav4@pitt.edu
Web page: http://www.math.pitt.edu/~annav/math3020.html

                                                                        Every problem of the calculus of variations has a solution
                                                                           provided that the word "solution" is suitably understood.
                                                                                                                        David Hilbert

This course is an introduction to calculus of variations and some of its modern applications in science and engineering. Topics to be covered include variations of functionals, necessary and sufficient conditions for weak and strong extrema, canonical form of the Euler-Lagrange equations, principle of least action, conservation laws and direct methods of calculus of variations.  Extensions to the functionals involving higher-order derivatives, variable regions and multiple integrals will be considered.  The course will emphasize applications of these ideas to some problems in mechanics, such as vibrations of a membrane and phase transitions.

Text: Calculus of variations, by I. M. Gelfand and S.V. Fomin, Dover Publications, 2000.

In this course, we will mostly follow the format of this excellent book, although as in other graduate courses, additional material will be drawn from other sources. The paperback edition of Gelfand and Fomin is currently available at Amazon.com for $8.76. For additional reading, I also recommend

Robert Weinstock. Calculus of variations with applications to physics and engineering. Dover, 1974.
L. C. Young. Lectures on the calculus of variations and optimal control theory. Philadelphia, Saunders, 1969.
Charles Fox. An introduction to the calculus of variations. Dover, 1987.
Donald Smith. Variational methods in optimization. Dover, 1998.

go to the homework assignments

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