Certain 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 ...
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Certain 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.
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Seller's Description:
Mathematics/Diagrams/Graphs. Near Fine. Ex-Library Hardcover. 8vo-over 7¾"-9¾" tall. Retired library copy, usual stamps and markings; Textblock is clean and tight. Couple library labels on front cover, minimally shelf worn. 120pp., including bibliography and index.
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Seller's Description:
Very good in Good jacket. Volume 55 only. Jacket is lightly sunned and lightly worn along edges. Original price clipped from front jacket flap and price sticker from previous seller on front jacket flap as well. Previous owner's name written on top corner of first end page. Inside pages are clean and unmarked.
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Seller's Description:
Very good. 8vo, hardcover. No dj, blue cloth. Vg condition. Previous owner's name on front endpaper; covers and contents clean, no marking or writing. Binding square and tight. 119 pp.