This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topi... read more
Introduction to the Calculus of Variations by Hans Sagan Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
An Introduction to the Calculus of Variations by L.A. Pars Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Calculus of Variations by Lev D. Elsgolc This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.
Technical Calculus with Analytic Geometry by Judith L. Gersting Well-conceived text with many special features covers functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, much more. Many examples, exercises, practice problems, with answers. Advanced undergraduate/graduate-level. 1984 edition.
An Introduction to the Calculus of Variations by Charles Fox Highly regarded text for advanced undergraduate and graduate students explores first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.
This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.
Robert Weinstock's Calculus of Variations, first published by McGraw-Hill in 1952 and reprinted by Dover in 1974, is one of Dover's longest-running books in mathematics. In a memoir written in the 1990s, Weinstock recalled how, after he received his PhD in physics from Stanford in 1943, he worked for a time at Harvard's Radar Research Laboratory as part of the war effort. Describing himself then as an idealistic 26-year-old, he came up with the idea that he could do more for humanity and humanity's problems as a working man than as a physicist, and so went to work for some months in 1946 as a seaman on two merchant ships.
Back in the United States, Weinstock responded to a call for qualified mathematics instructors at Stanford (then, like most American colleges and universities, dealing with a major influx of new students supported by the GI Bill). He planned at the time to return to academia for only a short time. But, as it turned out, a long teaching career at Stanford, Notre Dame, and finally Oberlin ensued, concluding in 1990 after about fifty years. In the Author's Own Words: "From January into September 1946, I was a wiper (an engine-room worker who did painting, cleaning, and other maintenance) on a succession of two merchant ships. These took me twice through the Panama Canal and provided visits to all three World War Two enemy nations: Italy, Germany, and Japan. I experienced what were surely the most fascinating eight months of my life. I'm convinced, in retrospect, that I was in 1946 the only wiper in the U.S.Merchant Marine with a PhD in physics." — Robert Weinstock
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