Verwandte Artikel zu Introduction To The Calculus Of Variations (1917)
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Inhaltsangabe
Introduction to the Calculus of Variations is a book written by William Elwood Byerly in 1917. The book provides an introduction to the calculus of variations, which is a branch of mathematics concerned with finding the optimal solution to a functional. The book covers topics such as the Euler-Lagrange equation, the Hamiltonian principle, and the Jacobi condition. It also includes examples and exercises to help readers understand the concepts. The book is written in a clear and concise manner, making it accessible to both students and professionals in the field of mathematics. Overall, Introduction to the Calculus of Variations is a valuable resource for anyone interested in learning about this important branch of mathematics.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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Reseña del editor
This scarce antiquarian book is a facsimile reprint of the original. 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 for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
Reseña 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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