{"product_id":"9781461348191","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003eGaiko, V.\u003c\/h2\u003e \u003cp\u003eOn the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk \"Mathematical problems\" at the Second Interna­ tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema­ tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi­ cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi­ nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi­ ble complete information on the qualitative behaviour of integral curves defined by this equation (176].\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2013-11-22\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461348191\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4419-9168-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 182\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":46539718918284,"sku":"9781461348191","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461348191.jpg?v=1775679647","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781461348191","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}