Techniques of asymptotic analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1971
|
| Series: | Applied mathematical sciences
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 306 S. Ill., graph. Darst. |
| ISBN: | 0387900225 3540900225 |
Staff View
MARC
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| 490 | 1 | |a Applied mathematical sciences |v 2 | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
PREFACE v
CHAPTER 1. ASYMPTOTIC SEQUENCES AND ASYMPTOTIC DEVELOPMENT
OF A FUNCTION
1.1. Notation and Definition 1
1.2. Operations with Asymptotic Expansions 11
Asymptotic Integration 17
Differentiation 21
1.3. Some Remarks on the Use of Asymptotic Expansions ... 24
l.U. Summation of Asymptotic Expansions 28
CHAPTER 2. THE ASYMPTOTIC DEVELOPMENT OF A FUNCTION DEFINED
BY AN INTEGRAL
2.1. Elementary Analytic Methods 38
Analytic Continuation of Functions Defined
by an Integral 38
Integration by Parts 40
Asymptotic Evaluation of Indefinite Integrals .... 44
Asymptotic Evaluation of Integrals of the
Form / f(x,t)dt 54
2.2. Laplace and Fourier Transforms at Infinity 62
Watson1s Lemma 65
Fourier Integrals 74
2.3. Laplace s Formula and Its Generalization 80
2.k. Kelvin s Formula and Generalizations 86
2.5. Integrals of the Type /P[~^G(x,t)dt 95
Generalized Laplace Formula 96
Generalized Kelvin s Formula 100
Dispersive Wave Propagation 102
2.6. Method of Steepest Descents and the
Saddle Point Formula 105
Saddle Point Method for a Complex
Large Parameter 115
The Complete Asymptotic Development 117
Application to Bessel Functions 122
2.7. Applications of the Saddle Point Method 126
The Airy Integral 126
A Generalization of the Airy Integral 134
2.8. Multidimensional Integrals: Part I.
Laplace, Kelvin, and Related Formulas 136
2.9. Multidimensional Integrals: Part II.
Many Parameters 148
Complete Asymptotic Development 155
2.10. Asymptotic Evaluation of Integrals
Involving Non-Uniformities . l64
Integrals Containing a Global Maximum
Near an Endpoint 165
Neighboring Saddle Points 170
2.11. Miscellaneous 176
Laplace Transforms in the Neighborhood of
the Origin 176
Fourier Transforms at the Origin 181
Bromwich Integrals at Infinity 182
Bromwich Integrals at the Origin 186
CHAPTER 3. LINEAR ORDINARY DIFFERENTIAL EQUATIONS
3.0. Introduction 189
3.1. Some Topics in Matrix Analysis 192
Applications to Ordinary Differential Equations . . . 195
3.2. Matrix Theory - Continued 201
Functions of Matrices 207
Dunford-Taylor Integral 210
Construction of a Function of a Matrix 211
3.3. Linear Ordinary Differential Equations with
Constant Coefficients 219
3 A. Classification and General Properties of Ordinary
Differential Equations in the Neighborhood of
Singular Points 226
Circuit Relations 230
Singular Points of an n Order Sealer Ordinary
Differential Equations 232
Solutions in the Neighborhood of Infinity 234
dX
The Equation z -Z. = A X 235
dz ~o~ • • • 240
3.5. Linear Ordinary Differential Equations with
Regular Singular Points 240
The Case of a Sealer Ordinary Differential
Equation with a Regular Singular Point 254
Method of Frobenius 256
3.6. Irregular Singular Points 259
Sealer Ordinary Differential Equations 278
Second Order Equations 284
3.7- Ordinary Differential Equations Containing
a Large Parameter 289
Formal Solution 289
Turning or Transition Points 292
Connection Formulas 294
Langer s Uniform Method 296
READING LIST 300
INDEX 301
|
| any_adam_object | 1 |
| author | Sirovich, L. 1933- |
| author_GND | (DE-588)1145536263 |
| author_facet | Sirovich, L. 1933- |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV002965253 |
| callnumber-first | Q - Science |
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| dewey-full | 515/.234 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.234 |
| dewey-search | 515/.234 |
| dewey-sort | 3515 3234 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:51:31Z |
| institution | BVB |
| isbn | 0387900225 3540900225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001856539 |
| oclc_num | 301526825 |
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| physical | IX, 306 S. Ill., graph. Darst. |
| psigel | HUB-ZB011201109 |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Sirovich, L. 1933- Verfasser (DE-588)1145536263 aut Techniques of asymptotic analysis L. Sirovich New York [u.a.] Springer 1971 IX, 306 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 2 Analyse fonctionnelle Analyse mathématique ram Développements asymptotiques ram Equation differentielle lineaire obspm Équations différentielles Analysis (DE-588)4001865-9 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Analysis (DE-588)4001865-9 s Asymptotische Methode (DE-588)4287476-2 s Applied mathematical sciences 2 (DE-604)BV000005274 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001856539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sirovich, L. 1933- Techniques of asymptotic analysis Applied mathematical sciences Analyse fonctionnelle Analyse mathématique ram Développements asymptotiques ram Equation differentielle lineaire obspm Équations différentielles Analysis (DE-588)4001865-9 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4112609-9 (DE-588)4287476-2 |
| title | Techniques of asymptotic analysis |
| title_auth | Techniques of asymptotic analysis |
| title_exact_search | Techniques of asymptotic analysis |
| title_full | Techniques of asymptotic analysis L. Sirovich |
| title_fullStr | Techniques of asymptotic analysis L. Sirovich |
| title_full_unstemmed | Techniques of asymptotic analysis L. Sirovich |
| title_short | Techniques of asymptotic analysis |
| title_sort | techniques of asymptotic analysis |
| topic | Analyse fonctionnelle Analyse mathématique ram Développements asymptotiques ram Equation differentielle lineaire obspm Équations différentielles Analysis (DE-588)4001865-9 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| topic_facet | Analyse fonctionnelle Analyse mathématique Développements asymptotiques Equation differentielle lineaire Équations différentielles Analysis Asymptotische Entwicklung Asymptotische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001856539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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