Euler-Lagrange Equation | Calculus of variations, Differential equation, Function (mathematics), Functional (mathematics), Stationary point, Leonhard Euler, Joseph Louis Lagrange, Maxima and minima, Optimization (mathematics)

Frederic P. Miller (u. a.)

ISBN 10: 6130252854 / ISBN 13: 9786130252854

Published by OmniScriptum, 2026

About this Item

Euler-Lagrange Equation | Calculus of variations, Differential equation, Function (mathematics), Functional (mathematics), Stationary point, Leonhard Euler, Joseph Louis Lagrange, Maxima and minima, Optimization (mathematics) | Frederic P. Miller (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130252854 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Seller Inventory # 101407661

Bibliographic Details

• Title: Euler-Lagrange Equation | Calculus of variations, Differential equation, Function (mathematics), Functional (mathematics), Stationary point, Leonhard Euler, Joseph Louis Lagrange, Maxima and minima, Optimization (mathematics)
• Publisher: OmniScriptum
• Publication Date: 2026
• Language: English
• ISBN 10: 6130252854
• ISBN 13: 9786130252854
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 11D millimeters 220 millimeters width by 150 millimeters height by 11 millimeters depth
• Weight: 268 grams
• Seller catalogs:
  • Bücher

About this title

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).