{"product_id":"topological-methods-for-differential-equations-john-r-graef-9781138332294","title":"Topological Methods for Differential Equations and Inclusions","description":"\u003cp\u003e\u003cem\u003eTopological Methods for Differential Equations and Inclusions\u003c\/em\u003e covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e John R. Graef,Johnny Henderson,Abdelghani Ouahab\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1138332291\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781138332294\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e CRC Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/02\/2018\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 360\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.75lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.10h x 7.10w x 1.00d","brand":"John R. Graef","offers":[{"title":"Hardcover","offer_id":48113274519807,"sku":"9781138332294","price":225.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_4573ac2c-a620-4232-be6c-eb9c37e8cd46.jpg?v=1769614021","url":"https:\/\/www.whiterainbookhouse.com\/products\/topological-methods-for-differential-equations-john-r-graef-9781138332294","provider":"WR Book House","version":"1.0","type":"link"}