Euler?Lagrange Equation: Calculus of variations, Differential equation, Function (mathematics), Functional (mathematics), Stationary point, Leonhard ... Maxima and minima, Optimization (mathematics) - Couverture souple

Couverture souple

ISBN 10 : 6130252854 ISBN 13 : 9786130252854

Editeur : Alphascript Publishing, 2009

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In calculus of variations, the Euler–Lagrange equation, or Lagrange's equation, is a differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italo-French mathematician Joseph Louis Lagrange in the 1750s. Because a differentiable functional is stationary at its local maxima and minima, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing (or maximizing) it. This is analogous to Fermat's theorem in calculus, stating that where a differentiable function attains its local extrema, its derivative is zero. In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler–Lagrange equation for the action of the system. In classical mechanics, it is equivalent to Newton's laws of motion, but it has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations (see, for example, the "Field theory" section below).

Détails de l'édition

• Éditeur: Alphascript Publishing
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 6130252854
• ISBN 13: 9786130252854
• Reliure: Broché
• Nombre de pages: 168
• Éditeur: Miller Frederic P., Vandome Agnes F., McBrewster John
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible