Introduction to asymptotics: a treatment using nonstandard analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1997
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 165 S. graph. Darst. |
| ISBN: | 9810229151 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | INTRODUCTION TO ASYMPTOTICS A TREATMENT USING NONSTANDARD ANALYSIS
CONTENTS PREFACE VII 1 BASIC THEORY 1 1.1 INTRODUCTION 1 1.2 ASYMPTOTIC
SEQUENCES 3 1.3 ASYMPTOTIC EXPANSIONS 5 1.4 OPERATIONS ON ASYMPTOTIC
EXPANSIONS 7 1.5 POWER SERIES 10 1.6 A GENERALISATION 12 1.7 AN
ILLUSTRATION 13 EXERCISES ON CHAPTER 1 15 2 INTEGRALS , - 17 2.1
STIRLING S FORMULA 17 2.2 LAPLACE INTEGRALS 23 2.3 LAPLACE-TYPE
INTEGRALS 26 2.4 COMPLEX CONTOURS 27 2.5 FOURIER INTEGRALS 32 2.6 METHOD
OF STATIONARY PHASE 38 2.7 EXPANSIONS .40 EXERCISES ON CHAPTER 2 41 3
SERIES 43 3.1 GENERAL RESULTS 43 3.2 POWER SERIES 49 3.3 PARTIAL SUMS 53
3.4 ASYMPTOTIC BEHAVIOUR OF AN ENTIRE FUNCTION 59 3.5 PARTIAL SUMS OF
INTEGRALS 65 3.6 MACLAURIN SERIES 70 3.7 OPTIMAL REMAINDERS 73 EXERCISES
ON CHAPTER 3 75 4 UNIFORM ASYMPTOTICS 79 4.1 A SIMPLE EXAMPLE 79 4.2 THE
FUNCTION J 79 4.3 POLE NEAR A SADDLE POINT 87 4.4 SADDLE POINT NEAR AN
ENDPOINT 89 4.5 COALESCING SADDLE POINTS 92 IX EXERCISES ON CHAPTER 4 95
HYPERASYMPTOTICS 99 5.1 INTRODUCTION 99 5.2 A LAPLACE INTEGRAL 100 5.3
EXTENSIONS 108 5.4 STIELTJES TRANSFORMS 110 5.5 STOKES PHENOMENON 113
EXERCISES ON CHAPTER 5 118 DIFFERENTIAL EQUATIONS 119 6.1 THE WKB
APPROXIMATION 119 6.2 AN ERROR BOUND FOR THE WKB APPROXIMATION 120 6.3
EFFECT OF A PARAMETER 123 6.4 SOLUTIONS IN SERIES 126 6.5 AN ERROR BOUND
FOR THE SERIES 129 6.6 CONNECTION FORMULAE --. 133 6.7 HYPERASYMPTOTICS
135 6.8 PARAMETER WITH ZERO 136 EXERCISES ON CHAPTER 6 137 INTRODUCTION
TO NONSTANDARD ANALYSIS 141 A.I BASIC IDEAS 141 A.2 SEQUENCES 146 A.3
CONTINUITY 149 A.4 THE DERIVATIVE 151 A.5 INTEGRATION 154 REFERENCES 159
INDEX 161
|
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| author | Jones, Douglas S. |
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| dewey-ones | 516 - Geometry 519 - Probabilities and applied mathematics |
| dewey-raw | 516.362 519.2/4 |
| dewey-search | 516.362 519.2/4 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:21:53Z |
| institution | BVB |
| isbn | 9810229151 |
| language | English |
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| publishDate | 1997 |
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| spelling | Jones, Douglas S. Verfasser aut Introduction to asymptotics a treatment using nonstandard analysis D. S. Jones Singapore [u.a.] World Scientific 1997 X, 165 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Asymptotisch gedrag gtt Reeksontwikkelingen gtt Asymptotic expansions Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Asymptotik (DE-588)4126634-1 s Nonstandard-Analysis (DE-588)4137021-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008201658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jones, Douglas S. Introduction to asymptotics a treatment using nonstandard analysis Asymptotisch gedrag gtt Reeksontwikkelingen gtt Asymptotic expansions Nonstandard-Analysis (DE-588)4137021-1 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)4126634-1 |
| title | Introduction to asymptotics a treatment using nonstandard analysis |
| title_auth | Introduction to asymptotics a treatment using nonstandard analysis |
| title_exact_search | Introduction to asymptotics a treatment using nonstandard analysis |
| title_full | Introduction to asymptotics a treatment using nonstandard analysis D. S. Jones |
| title_fullStr | Introduction to asymptotics a treatment using nonstandard analysis D. S. Jones |
| title_full_unstemmed | Introduction to asymptotics a treatment using nonstandard analysis D. S. Jones |
| title_short | Introduction to asymptotics |
| title_sort | introduction to asymptotics a treatment using nonstandard analysis |
| title_sub | a treatment using nonstandard analysis |
| topic | Asymptotisch gedrag gtt Reeksontwikkelingen gtt Asymptotic expansions Nonstandard-Analysis (DE-588)4137021-1 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Asymptotisch gedrag Reeksontwikkelingen Asymptotic expansions Nonstandard-Analysis Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008201658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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