Introduction To The Calculus Of Variations (1917) - Softcover

Byerly, William Elwood

Softcover

ISBN 10: 1437025471 ISBN 13: 9781437025477

Verlag: Kessinger Publishing, LLC, 2008

Inhaltsangabe

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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
• Sprache: Englisch
• ISBN 10: 1437025471
• ISBN 13: 9781437025477
• Einband: Tapa blanda
• Anzahl der Seiten: 56
• Kontakt zum Hersteller: Nicht verfügbar
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