{"product_id":"asymptotic-expansions-paperback-9780521604826","title":"Asymptotic Expansions (Paperback) 9780521604826","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAsymptotic Expansions\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAsymptotic representation of a function os of great importance in many branches of pure and applied mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eE. T. Copson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521604826, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 3 June 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e132 pages\u003cbr\u003e21.5 x 14.2 x 0.9 cm, 0.18 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eCertain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of pure and applied mathematics and in theoretical physics. Solutions of ordinary differential equations are frequently obtained in the form of a definite integral or contour integral, and this tract is concerned with the asymptotic representation of a function of a real or complex variable defined in this way. After a preliminary account of the properties of asymptotic series, the standard methods of deriving the asymptotic expansion of an integral are explained in detail and illustrated by the expansions of various special functions. These methods include integration by parts, Laplace's approximation, Watson's lemma on Laplace transforms, the method of steepest descents, and the saddle-point method. The last two chapters deal with Airy's integral and uniform asymptotic expansions.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Preliminaries\u003cbr\u003e 3. Integration by parts\u003cbr\u003e 4. The method of stationary phase\u003cbr\u003e 5. The method of Laplace\u003cbr\u003e 6. Watson's lemma\u003cbr\u003e 7. The method of steepest descents\u003cbr\u003e 8. The saddle-point method\u003cbr\u003e 9. Airy's integral\u003cbr\u003e 10. Uniform asymptotic expansions\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46129226187032,"sku":"9780521604826","price":34.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521604826i.jpg?v=1691666391","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/asymptotic-expansions-paperback-9780521604826","provider":"Freshly Printed Books","version":"1.0","type":"link"}