Asymptotic methods for integrals:
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtai...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub. Co.
c2015
|
| Series: | Series in analysis
vol. 6 |
| Subjects: | |
| Online Access: | FHN01 Volltext |
| Summary: | This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on |
| Physical Description: | xxii, 605 p. ill |
| ISBN: | 9789814612166 |
Staff View
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| 520 | |a This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on | ||
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| id | DE-604.BV044640408 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:58Z |
| institution | BVB |
| isbn | 9789814612166 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030038381 |
| oclc_num | 988732328 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xxii, 605 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| series2 | Series in analysis |
| spelling | Temme, Nico M. 1940- Verfasser aut Asymptotic methods for integrals Nico M. Temme Singapore World Scientific Pub. Co. c2015 xxii, 605 p. ill txt rdacontent c rdamedia cr rdacarrier Series in analysis vol. 6 This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on Integral equations / Asymptotic theory Differential equations / Asymptotic theory Functions, Special Integralgleichung (DE-588)4027229-1 gnd rswk-swf Asymptotische Approximation (DE-588)4739184-4 gnd rswk-swf Integralgleichung (DE-588)4027229-1 s Asymptotische Approximation (DE-588)4739184-4 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789814612159 http://www.worldscientific.com/worldscibooks/10.1142/9195#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Temme, Nico M. 1940- Asymptotic methods for integrals Integral equations / Asymptotic theory Differential equations / Asymptotic theory Functions, Special Integralgleichung (DE-588)4027229-1 gnd Asymptotische Approximation (DE-588)4739184-4 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4739184-4 |
| title | Asymptotic methods for integrals |
| title_auth | Asymptotic methods for integrals |
| title_exact_search | Asymptotic methods for integrals |
| title_full | Asymptotic methods for integrals Nico M. Temme |
| title_fullStr | Asymptotic methods for integrals Nico M. Temme |
| title_full_unstemmed | Asymptotic methods for integrals Nico M. Temme |
| title_short | Asymptotic methods for integrals |
| title_sort | asymptotic methods for integrals |
| topic | Integral equations / Asymptotic theory Differential equations / Asymptotic theory Functions, Special Integralgleichung (DE-588)4027229-1 gnd Asymptotische Approximation (DE-588)4739184-4 gnd |
| topic_facet | Integral equations / Asymptotic theory Differential equations / Asymptotic theory Functions, Special Integralgleichung Asymptotische Approximation |
| url | http://www.worldscientific.com/worldscibooks/10.1142/9195#t=toc |
| work_keys_str_mv | AT temmenicom asymptoticmethodsforintegrals |