![]() ![]() History of the Calculus of Variations in the 18th Century. A Treatise on Isoperimetal Problems and the Calculus of Variations. $?.Ĭalculus of Variations, with Applications to Physics and Engineering. History of the Calculus of Variations During the Nineteenth Century. Princeton, NJ: Princeton University Press, 1989. One of the fathers of string theory, he is the author of The Black Hole War and The Cosmic Landscape. Plateau's Problem and the Calculus of Variations. Leonard Susskind has been the Felix Bloch Professor in Theoretical Physics at Stanford University since 1978, and his online lectures are viewed all around the world. ![]() Introduction to the Calculus of Variations. The Hamilton-Jacobi Theory in the Calculus of Variations: Its Role in Mathematics and Physics. The integral I(y) is an example of a functional, which (more generally) is a mapping from a set of allowable functions to the reals. An Introduction to the Calculus of Variations. A typical problem in the calculus of variations involve finding a particular function y(x) to maximize or minimize the integral I(y) subject to boundary conditions y(a) A and y(b) B. ``What is the Calculus of Variations and What are its Applications.''In The Variational Principles of Mechanics, 4th ed. Contains a dense mathematical treatment but with many examples. London: Butterworths Scientific Publications, 1952. Calculus of Variations by Parallel Displacement. Contains excellent accessible discussions of the problems and history of the calculus of variations. The Science of Soap Films and Soap Bubbles. Lecons sur le calcul des variations professees par J. Includes discussions of historical derivations which are very difficult to decipher. $159.Ī History of the Calculus of Variations from the 17th through the 19th Century. Giaquinta, Mariano and Hildebrandt, Stefan.Ĭalculus of Variations. Gelfand, Izrail Moiseevich and Fomin, Sergei Vasilevich.Įnglewood Cliffs, NJ: Prentice-Hall, 1963. ![]() Excellent, detailed mathematical treatment, now unfortunately out of print.Īn Introduction to the Calculus of Variations. Dense and mimeographed.Ĭalculus of Variations with Applications.įorsyth, Andrew Russell. $76.Ĭalculus of Variations and Partial Differential Equations of the First Order, 2 vols, 2nd ed. Chicago, IL: University of Chicago Press, 1961. Emphasis is on abstract mathematics (fields), not applications. Considered by some a classic, but its rambling style makes it difficult to read. Now out in 4th ed.Ĭhicago, IL: Published for the Math. 17 in Mathematical Methods for Physicists, 3rd ed. See also Calculus of Variations, Minimal SurfacesĪrfken, George. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.Calculus of Variations - from Eric Weisstein's Encyclopedia of Scientific Books While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. Calculus of Variations (ISSN) - Kindle edition by Elsgolc, L. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. ![]() This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. ![]()
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