Asymptotics of linear differential equations:
Asymptotic methods' use of several important phenomena of nature can be explained. The main problems considered in the text are based on the notion of an asymptotic space, which was introduced by the author in his works.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2001
|
| Schriftenreihe: | Mathematics and its applications
533 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Asymptotic methods' use of several important phenomena of nature can be explained. The main problems considered in the text are based on the notion of an asymptotic space, which was introduced by the author in his works. |
| Beschreibung: | IX, 441 S. |
| ISBN: | 0792371933 |
Internformat
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Datensatz im Suchindex
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| adam_text | ASYMPTOTICS OF LINEAR DIFFERENTIAL EQUATIONS BY M.H. LANTSMAN KLUWER
ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE IX
CHAPTER 1. INTRODUCTION 1 1. INTRODUCTION 1 2. CONVENTIONS AND NOTATION
5 3. ASYMPTOTIC RELATIONS 9 3.1 DEFINITION OF ASYMPTOTICS 9 3.2 MAIN
ASYMPTOTIC RELATIONS 11 CHAPTER 2. METRIC SPACES 14 1. MAIN DEFINITIONS
14 2. SEVERAL EXAMPLES OF METRIC SPACES 16 3. SEQUENCES IN A METRIC
SPACE 17 4. EQUATIONS IN A METRIC SPACE 22 5. ABSTRACT FUNCTIONS 23 6.
LINEAR SETS 24 7. METRIC GROUPS. MAIN ASYMPTOTIC RELATIONS IN A METRIC
GROUP 26 8. LINEAR SYSTEMS 27 9. NORMED SPACES 29 10. BASIC PROPERTIES
OF DEFINITE INTEGRALS 31 11. SOLUTION OF DIFFERENTIAL EQUATIONS 34
CHAPTER 3. ASYMPTOTIC SPACES 38 1. DEFINITION OF AN ASYMPTOTIC SPACE 38
2. EXAMPLES OF ASYMPTOTIC SPACES 39 3. SPACES OF TYPE HP 40 4. SERIES
AND SEQUENCES IN ASYMPTOTIC SPACES 43 5. FORMAL AND ASYMPTOTIC SOLUTIONS
44 6. FACTOR SPACES 46 CHAPTER 4. ASYMPTOTIC BEHAVIOUR OF FUNCTIONS 49
1. INFINITESIMAL FUNCTIONS OF A REAL ARGUMENT 50 2. ANALYTIC ESTIMATES
54 3. SERIES AND SEQUENCES IN THE SPACE II 56 VI ASYMPTOTICS OF LINEAR
DIFFERENTIAL EQUATIONS 4. OPERATORS IN THE SPACE II 63 5. DERIVATIVE
ESTIMATES 67 6. ASYMPTOTIC BEHAVIOUR OF ANALYTIC FUNCTIONS 71 7.
IMPLICIT FUNCTIONS 84 7.1 SOME GENERAL METHODS 84 7.2 LAGRANGE S FORMULA
85 CHAPTER 5. POWER ORDER GROWTH FUNCTIONS ON THE POSITIVE SEMI-AXIS 90
1. REGULARLY VARYING FUNCTIONS 90 2. CLASS A T 96 3. SUBSETS OF THE
CLASS AT WITH SOME ALGEBRAIC AND ANALYTIC PROPERTIES 103 4. ALGEBRAIC
EXTENSIONS OF FIELDS OF TYPE NG 106 5. ALGEBRAIC EXTENSIONS BY ROOTS OF
AN ALGEBRAIC SYSTEM 113 6. NON-ALGEBRAIC EXTENSIONS 116 7. ESTIMATES OF
ROOTS OF ALGEBRAIC EQUATIONS WITH COMPARABLE COEFFICIENTS 119 8.
OPERATORS IN A FIELD OF TYPE N 126 CHAPTER 6. POWER ORDER GROWTH
FUNCTIONS OF THE COMPLEX ARGUMENT 128 1. CLASSES A S AND A 128 2.
SUBSETS OF CLASS AS WITH SOME ALGEBRAIC AND ANALYTIC PROPERTIES 133 3.
POWER-LOGARITHMIC FUNCTIONS 137 CHAPTER 7. INTEGRALS 144 1. IMPROPER
INTEGRALS 144 2. INTEGRALS WITH A VARIABLE LIMIT 147 3. THE LAPLACE
TRANSFORMATION 153 4. THE LAPLACE METHOD 166 5. THE SADDLE POINT METHOD
171 CHAPTER 8. LINEAR DIFFERENTIAL EQUATIONS 183 1. SYSTEMS OF LINEAR
DIFFERENTIAL EQUATIONS 183 2. SINGLE LINEAR DIFFERENTIAL EQUATIONS OF
NTH ORDER 193 3. SUBSTITUTION X = YX 200 4. SYSTEM OF LINEAR
DIFFERENTIAL EQUATIONS IN THE COMPLEX PLANE 204 VLL CHAPTER 9. GENERAL
ASYMPTOTIC PROPERTIES OF LINEAR DIFFERENTIAL EQUATIONS 206 1. GENERAL
ESTIMATES 206 2. THE CASE WHEN THE COEFFICIENTS RAPIDLY TEND TO ZERO 211
3. ALMOST DIAGONAL AND L-DIAGONAL SYSTEMS 214 4. SINGLE LINEAR EQUATION
WITH ASYMPTOTICALLY SIMPLE ROOTS OF THE CHARACTERISTIC POLYNOMIAL 224
CHAPTER 10. LINEAR DIFFERENTIAL EQUATIONS WITH POWER ORDER GROWTH
COEFFICIENTS ON THE POSITIVE SEMI-AXIS 230 1. FORMAL SOLUTIONS TO A
SINGLE LINEAR DIFFERENTIAL EQUATION OF NTH ORDER 233 2. ASYMPTOTIC
SOLUTIONS TO A SINGLE LINEAR EQUATION OF NTH ORDER 247 3. QUALITATIVE
CHARACTERISTICS OF LINEAR DIFFERENTIAL EQUATIONS 256 4. SECOND ORDER
DIFFERENTIAL EQUATIONS 258 4.1 STANDARD PROCEDURE 26 6 5. SYSTEMS OF TWO
DIFFERENTIAL EQUATIONS WITH TWO UNKNOWNS 270 CHAPTER 11. LINEAR
DIFFERENTIAL EQUATIONS IN SINGULAR CASES ON THE POSITIVE SEMI-AXIS 273
1. ASYMPTOTICALLY INDEPENDENT FUNCTIONS 274 2. FORMAL ASYMPTOTIC
SOLUTIONS 276 3. CONNECTION BETWEEN CHARACTERISTIC ROOTS AND SOLUTIONS
OF A LINEAR DIFFERENTIAL EQUATION 282 4. ANALYTIC TRANSFORMATIONS 295
4.1 SEVERAL PROPERTIES OF MATRIX EQUATIONS 296 4.2 THEOREM OF
QUASI-DIAGONALIZATION 302 CHAPTER 12. LINEAR DIFFERENTIAL EQUATIONS IN A
SECTOR OF THE COMPLEX PLANE 307 1. FORMAL SOLUTIONS 308 2. SOME
AUXILIARY PROPOSITIONS 314 3. MAIN THEOREMS 320 4. QUALITATIVE
CHARACTERISTICS OF LINEAR DIFFERENTIAL EQUATIONS IN A SECTOR OF THE
COMPLEX PLANE 332 CHAPTER 13. LINEAR DIFFERENTIAL EQUATIONS WITH
POWER-LOGARITHMIC COEFFICIENTS 335 1. SOME AUXILIARY PROPOSITIONS 335 2.
MAIN THEOREMS 340 VIII ASYMPTOTICS OF LINEAR DIFFERENTIAL EQUATIONS 3.
DEFICIENCY INDICES OF CERTAIN DIFFERENTIAL OPERATORS 346 4. SYSTEMS OF
LINEAR DIFFERENTIAL EQUATIONS 349 CHAPTER~14. LINEAR DIFFERENCE
EQUATIONS. GENERAL THEORY 354 1. FIRST ORDER EQUATIONS 355 1.1 SOME
AUXILIARY PROPOSITIONS 355 1.2 BERNOULLI NUMBERS 357 1.3 THE
EULER-MACLAURIN FORMULA 359 1.4 NON-HOMOGENEOUS EQUATIONS 362 2. SYSTEMS
OF NTH ORDER EQUATIONS 365 3. SINGLE LINEAR DIFFERENCE EQUATIONS OF NTH
ORDER 371 4. DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS 374 CHAPTER
15. ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF LINEAR DIFFERENCE EQUATIONS 378
1. THE POINCARE AND PERRON THEOREMS 380 1.1 THE POINCARE THEOREM 384 1.2
PERRON S THEOREM 388 2. LINEAR DIFFERENCE EQUATIONS WITH POWER ORDER
GROWTH COEFFICIENTS 392 3. ASYMPTOTIC SOLUTION TO LINEAR DIFFERENCE
EQUATION 398 4. SECOND ORDER EQUATIONS 402 5. SYSTEMS OF TWO EQUATIONS
411 6. HIGHER ORDER EQUATIONS 413 7. DIFFERENTIAL-DIFFERENCE EQUATIONS
417 CHAPTER 16. SUPPLEMENT 420 1. ALGORITHMS WITH AN UNIFORMLY
DISTRIBUTED THEORETICAL ERROR 420 BIBLIOGRAPHY 425 LIST OF SYMBOLS 437
INDEX 438
|
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| id | DE-604.BV014168646 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:58:55Z |
| institution | BVB |
| isbn | 0792371933 |
| language | English |
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| owner_facet | DE-703 DE-824 |
| physical | IX, 441 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Lantsman, M. H. Verfasser aut Asymptotics of linear differential equations by M. H. Lantsman Dordrecht [u.a.] Kluwer Acad. Publ. 2001 IX, 441 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 533 Asymptotic methods' use of several important phenomena of nature can be explained. The main problems considered in the text are based on the notion of an asymptotic space, which was introduced by the author in his works. Differential equations, Linear Asymptotic theory Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s Asymptotik (DE-588)4126634-1 s DE-604 Mathematics and its applications 533 (DE-604)BV008163334 533 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009712521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lantsman, M. H. Asymptotics of linear differential equations Mathematics and its applications Differential equations, Linear Asymptotic theory Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4353441-7 (DE-588)4126634-1 |
| title | Asymptotics of linear differential equations |
| title_auth | Asymptotics of linear differential equations |
| title_exact_search | Asymptotics of linear differential equations |
| title_full | Asymptotics of linear differential equations by M. H. Lantsman |
| title_fullStr | Asymptotics of linear differential equations by M. H. Lantsman |
| title_full_unstemmed | Asymptotics of linear differential equations by M. H. Lantsman |
| title_short | Asymptotics of linear differential equations |
| title_sort | asymptotics of linear differential equations |
| topic | Differential equations, Linear Asymptotic theory Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Differential equations, Linear Asymptotic theory Lineare gewöhnliche Differentialgleichung Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009712521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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