{"product_id":"variational-principles-for-second-order-differential-joseph-grifone-9789810237349","title":"Variational Principles for Second-Order Differential Equations, Application of the Spencer Theory of","description":"The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Joseph Grifone,Zoltan Muzsnay\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9810237340\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789810237349\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/26\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 228\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.01lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 8.84h x 6.32w x 0.76d","brand":"Joseph Grifone","offers":[{"title":"Hardcover","offer_id":48448092012799,"sku":"9789810237349","price":95.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5b7b21db-6540-42fd-a4f9-50a5ecd197f2.jpg?v=1777236841","url":"https:\/\/www.whiterainbookhouse.com\/products\/variational-principles-for-second-order-differential-joseph-grifone-9789810237349","provider":"WR Book House","version":"1.0","type":"link"}