Asymptotic methods in the theory of linear differential equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
American Elsevier
1967
|
| Schriftenreihe: | Modern analytic and computational methods in science and mathematics
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XVI, 270 S. |
Internformat
MARC
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| 100 | 1 | |a Feščenko, Stepan F. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Asimptotičeskie metody v teorii linejnych differencial'nych uravnenij |
| 245 | 1 | 0 | |a Asymptotic methods in the theory of linear differential equations |c by S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko. Transl. by Scirpta Technica, Inc. Transl. ed: Herbert Eagle |
| 264 | 1 | |a New York |b American Elsevier |c 1967 | |
| 300 | |a XVI, 270 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Modern analytic and computational methods in science and mathematics |v 10 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Differential equations, linear | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 0 | 7 | |a Asymptotische Methode |0 (DE-588)4287476-2 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Lineare Differentialgleichung |0 (DE-588)4206889-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 1 | |a Asymptotische Methode |0 (DE-588)4287476-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Lineare Differentialgleichung |0 (DE-588)4206889-7 |D s |
| 689 | 1 | 1 | |a Asymptotische Methode |0 (DE-588)4287476-2 |D s |
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| 700 | 1 | |a Škilʹ, Mykola Ivanovyč |d 1932- |e Verfasser |0 (DE-588)130399078 |4 aut | |
| 700 | 1 | |a Nikolenko, L. D. |e Verfasser |4 aut | |
| 700 | 1 | |a Eagle, Herbert |e Sonstige |4 oth | |
| 830 | 0 | |a Modern analytic and computational methods in science and mathematics |v 10 |w (DE-604)BV001888148 |9 10 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-004527096 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804121296826531840 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION ix
1. CONSTRUCTION OF ASYMPTOTIC SOLUTIONS FOR SECOND
ORDER LINEAR DIFFERENTIAL EQUATIONS WITH SLOWLY
VARYING COEFFICIENTS 1
1. Formulation of the Problem 1
2. A Formal Solution in the Case of Resonance 3
3. A Formal Solution in the Nonresonance Case 6
4. The Asymptotic Nature of the Solution 8
5. Finding the Tension in a Visco Elastic Thread of Variable
Length 16
2. CONSTRUCTION OF AN ASYMPTOTIC SOLUTION FOR A
SYSTEM OF SECOND ORDER LINEAR DIFFERENTIAL
EQUATIONS WITH SLOWLY VARYING COEFFICIENTS 25
6. Formulation of the Problem 25
7. A Formal Solution in the Resonance Case 26
8. The Nonresonance Case 35
9. The Asymptotic Nature of the Solution 36
10. On the Dynamic Stresses in a Visco Elastic Thread of
Variable Length with a Weight Q at the End 42
11. The Boundary Value Problem for a System of Second Order
Linear Differential Equations 54
3. ASYMPTOTIC DECOMPOSITION OF A SYSTEM OF LINEAR
DIFFERENTIAL EQUATIONS 61
12. Formulation of the Problem 61
13. Formal Decomposition 62
14. Construction of the Transforming Matrix and Differentiability
of the Formal Solution 66
15. Proof of Asymptotic Convergence 73
16. Some Special Cases of Decomposition 77
VIII CONTENTS
17. Decomposition of a Nonhomogeneous System of Linear
Differential Equations 79
18. Asymptotic Decomposition of a System of Ordinary Linear
Differential Equations in the Case of Multiple Roots of the
Characteristic Equation 85
4. CONSTRUCTION OF AN ASYMPTOTIC SOLUTION IN THE
CASE OF MULTIPLE ROOTS OF THE CHARACTERISTIC
EQUATION 121
19. General Remarks 121
20. The Case of Simple Elementary Divisors 123
21. A Formal Solution in the Presence of One Multiple
Elementary Divisor 125
22. An Example 142
23. The Asymptotic Nature of the Solution 146
24. Asymptotic Solution in the Presence of Several Multiple
Elementary Divisors 153
25. Construction of an Asymptotic Solution in the Case of
Other Sufficient Conditions 157
26. Differential Equations with a Small Parameter in the
Highest Derivatives 170
27. Finding the Characteristic Values of a Boundary Value
Problem for a Fourth Order Differential Equation Consisting
of Two Self Adjoint Expressions 173
5. ASYMPTOTIC SOLUTIONS OF DIFFERENTIAL EQUATIONS
IN BANACH SPACE 187
28. Formulation of the Problem 187
29. Existence and Uniqueness of the Solution 189
30. On the Solvability of Certain Operator Equations in
Banach Space 202
31. Construction of a Formal Solution 207
32. Proof of Asymptotic Convergence 213
33. Asymptotic Solutions of the Nonhomogeneous Equation 216
34. Direct Construction of a Particular Solution to the Non
homogeneous Equation 223
35. Applications 227
6. ASYMPTOTIC METHODS OF SOLVING LINEAR PARTIAL
DIFFERENTIAL EQUATIONS 239
36. Formulation of the Problem 239
37. Construction of Formal Solutions 243
38. Proof of Asymptotic Convergence 256
REFERENCES 261
INDEX 269
|
| any_adam_object | 1 |
| author | Feščenko, Stepan F. Škilʹ, Mykola Ivanovyč 1932- Nikolenko, L. D. |
| author_GND | (DE-588)130399078 |
| author_facet | Feščenko, Stepan F. Škilʹ, Mykola Ivanovyč 1932- Nikolenko, L. D. |
| author_role | aut aut aut |
| author_sort | Feščenko, Stepan F. |
| author_variant | s f f sf sff m i š mi miš l d n ld ldn |
| building | Verbundindex |
| bvnumber | BV007109569 |
| classification_rvk | SK 520 SK 910 |
| ctrlnum | (OCoLC)263566011 (DE-599)BVBBV007109569 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007109569 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:55:44Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004527096 |
| oclc_num | 263566011 |
| open_access_boolean | |
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| physical | XVI, 270 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | American Elsevier |
| record_format | marc |
| series | Modern analytic and computational methods in science and mathematics |
| series2 | Modern analytic and computational methods in science and mathematics |
| spelling | Feščenko, Stepan F. Verfasser aut Asimptotičeskie metody v teorii linejnych differencial'nych uravnenij Asymptotic methods in the theory of linear differential equations by S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko. Transl. by Scirpta Technica, Inc. Transl. ed: Herbert Eagle New York American Elsevier 1967 XVI, 270 S. txt rdacontent n rdamedia nc rdacarrier Modern analytic and computational methods in science and mathematics 10 Aus d. Russ. übers. Differential equations, linear Asymptotic expansions Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Lineare Differentialgleichung (DE-588)4206889-7 s 1\p DE-604 Škilʹ, Mykola Ivanovyč 1932- Verfasser (DE-588)130399078 aut Nikolenko, L. D. Verfasser aut Eagle, Herbert Sonstige oth Modern analytic and computational methods in science and mathematics 10 (DE-604)BV001888148 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004527096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Feščenko, Stepan F. Škilʹ, Mykola Ivanovyč 1932- Nikolenko, L. D. Asymptotic methods in the theory of linear differential equations Modern analytic and computational methods in science and mathematics Differential equations, linear Asymptotic expansions Asymptotische Methode (DE-588)4287476-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4012249-9 (DE-588)4206889-7 |
| title | Asymptotic methods in the theory of linear differential equations |
| title_alt | Asimptotičeskie metody v teorii linejnych differencial'nych uravnenij |
| title_auth | Asymptotic methods in the theory of linear differential equations |
| title_exact_search | Asymptotic methods in the theory of linear differential equations |
| title_full | Asymptotic methods in the theory of linear differential equations by S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko. Transl. by Scirpta Technica, Inc. Transl. ed: Herbert Eagle |
| title_fullStr | Asymptotic methods in the theory of linear differential equations by S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko. Transl. by Scirpta Technica, Inc. Transl. ed: Herbert Eagle |
| title_full_unstemmed | Asymptotic methods in the theory of linear differential equations by S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko. Transl. by Scirpta Technica, Inc. Transl. ed: Herbert Eagle |
| title_short | Asymptotic methods in the theory of linear differential equations |
| title_sort | asymptotic methods in the theory of linear differential equations |
| topic | Differential equations, linear Asymptotic expansions Asymptotische Methode (DE-588)4287476-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| topic_facet | Differential equations, linear Asymptotic expansions Asymptotische Methode Differentialgleichung Lineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004527096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001888148 |
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