Variational Calculus With Elementary Convexity - ISBN:0387907718

Variational Calculus With Elementary Convexity

Date: 24 April 2011, 00:53

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This book is intended as an introduction to the use of variational methods
in the formulation and solution of optimization problems of both mathe-
matical and physical interest. It is an outgrowth of lectures presented in the
Mathematics Department of Syracuse University during the past several
years. In preliminary form, the material from Chapters 0-6 comprised a
standard one-semester course of three hours per week given to upper-level
students in mathematics, physics, computer science, and engineering, and
that from the remainder of the book was offered on request during a succeed-
ing semester.
When pursued systematically, it is designed to carry those who have
completed a standard course in multidimensional calculus-with some
exposure to differential equations-through the rudiments of rigorous
analysis in (normed) linear spaces. For it is in the presence of the linear
spaces of continuously differentiable functions that a theory for the integral
inequalities which generated the calculus of variations can first be clarified.
In this setting, the fundamentals of the subject are explored, including the
natural role of the differential equations of Euler-Lagrange in relating the
behavior of integral inequalities to the physical principles of stationarity.

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