Introduction To The Calculus Of Variations (1917) - Softcover

Byerly, William Elwood

9781164824336: Introduction To The Calculus Of Variations (1917)

Softcover

ISBN 10: 1164824333 ISBN 13: 9781164824336

Verlag: Kessinger Publishing, 2010

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Introduction to the Calculus of Variations is a book written by William Elwood Byerly and first published in 1917. The book is a comprehensive introduction to the calculus of variations, which is a branch of mathematics that deals with finding the maximum or minimum of a functional, which is a function of a function. The book begins with an introduction to the basic concepts of the calculus of variations, including the Euler-Lagrange equation, which is used to find the function that minimizes or maximizes a given functional. It then goes on to cover a range of topics, including the calculus of variations for several variables, the calculus of variations for partial differential equations, and the calculus of variations for integral equations.Throughout the book, Byerly provides numerous examples and exercises to help readers understand the concepts and techniques of the calculus of variations. The book is written in a clear and concise style, making it accessible to both students and professionals in the field of mathematics.Overall, Introduction to the Calculus of Variations is a classic text in the field of mathematics and remains an important resource for anyone interested in the calculus of variations.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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Rese�a del editor

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

Rese�a del editor

The Calculus of Variations owed its origin to the attempt to solve a very interesting and rather narrow class of problems in Maxima and Minima, in which it is required to find the form of a function such that the definite integral of an expression involving that function and its derivative shall be a maximum or a minimum. Let us consider three simple examples: The Shortest Line, The Curve of Quickest Descent, and The Minimum Surface of Revolution. (a) The Shortest Line. Let it be required to find the equation of the shortest plane curve joining two given points. We shall use rectangular coordinates in the plane in question taking one of the points as the origin. Call the coordinates of the second point Xi, yi. If != fix) is a curve through (0, 0) and (xi, yi) and I is the length of the arc between the points, obviously I =v dx +dy a or 7= fv 1+ ydx, (1) and we wsh to determine the form of the function so that this integral shall be a minimum. (b) The Curve of Quickest Descent.
(Typographical errors above are due to OCR software and don't occur in the book.)

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