000 02536nam a22003738i 4500
001 CR9780511526121
003 UkCbUP
005 20200124160241.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090406s1965||||enk o ||1 0|eng|d
020 _a9780511526121 (ebook)
020 _z9780521047210 (hardback)
020 _z9780521604826 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA312
_b.C58 1965
082 0 4 _a515.35
_222
100 1 _aCopson, E. T.
_q(Edward Thomas),
_d1901-1980,
_eauthor.
245 1 0 _aAsymptotic expansions /
_cby E.T. Copson.
264 1 _aCambridge :
_bCambridge University Press,
_c1965.
300 _a1 online resource (120 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v55
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _aIntroduction -- Preliminaries -- Integration by parts -- The method of stationary phase -- The method of Laplace -- Watson's lemma -- The method of steepest descents -- The saddle-point method -- Airy's integral -- Uniform asymptotic expansions.
520 _aCertain 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.
650 0 _aAsymptotic expansions.
650 0 _aIntegrals.
776 0 8 _iPrint version:
_z9780521047210
830 0 _aCambridge tracts in mathematics ;
_v55.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511526121
999 _c518527
_d518525