Introduction To The Calculus Of Variations (1917) - Softcover

Byerly, William Elwood

Softcover

ISBN 10: 1437025471 ISBN 13: 9781437025477

Verlag: Kessinger Publishing, LLC, 2008

Inhaltsangabe

""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 study of calculus of variations, which is a branch of mathematics that deals with finding the optimal solution to a given problem. The book covers a range of topics including the basic principles of the calculus of variations, the Euler-Lagrange equation, the Hamiltonian formulation, and the variational methods in mechanics. It also includes a number of examples and exercises to help readers understand the concepts and apply them to real-world problems. The book is written in a clear and concise style, making it accessible to both beginners and advanced learners. It is a valuable resource for students and researchers in mathematics, physics, and engineering who want to gain a deeper understanding of 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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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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Details zur Ausgabe

• Verlag: Kessinger Publishing, LLC
• Erscheinungsdatum: 2008
• ISBN 10: 1437025471
• ISBN 13: 9781437025477
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 56
• Kontakt zum Hersteller: Nicht verfügbar