Ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, N.Y.
Dover Publ.
2009
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| Edition: | unabridged republ. of the work orig. publ. ... New York: Wiley, 1969 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 361 S. Ill. |
| ISBN: | 9780486472119 0486472116 |
Staff View
MARC
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| 245 | 1 | 0 | |a Ordinary differential equations |c Jack K. Hale |
| 250 | |a unabridged republ. of the work orig. publ. ... New York: Wiley, 1969 | ||
| 264 | 1 | |a Mineola, N.Y. |b Dover Publ. |c 2009 | |
| 300 | |a XIV, 361 S. |b Ill. | ||
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Record in the Search Index
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| adam_text | Contents CHAPTER 0. Mathematical preliminaries 0.1. Banach spaces and examples 0.2. Linear transformations 0.3. Fixed point theorems 1 1 3 4 CHAPTER I. General properties of differential equations 1.1. 1.2. 1.3. 1.4. 1.6. 1.6. 1.7. 1.8. 1.9. Existence Continuation of solutions Uniqueness and continuity properties Continuous dependence and stability Extension of the concept of a differential equation Differential inequalities Autonomous systems—generalities Autonomous systems—limit sets, invariant sets Remarks and suggestions for further study 12 12 16 18 25 28 30 37 46 49 CHAPTER II. Two dimensional systems ILL II.2. II.3. Planar two dimensional systems—the PoincaréBendixson theory Differential systems on a torus Remarks and suggestions for further study 31 51 64 76 CHAPTER III. Linear systems and linearization IILI. General linear systems 78 79
III.2. IIĪ.3. III.4. 111.6. ΙΙΙ.β. 111.7. 111.8. 111.9. 111.10. 111.11. Stability of linear and perturbed linear systems wth Order scalar equations Linear systems with constant coefficients Two dimensional linear autonomous systems The saddle point property Linear periodic systems Hill’s equation Reciprocal systems Canonical systems Remarks and suggestions for further study 83 89 93 101 106 117 121 131 136 142 CHAPTER IV. Perturbations of noncritical linear systems IV. 1. IV.2. IV.3. IV.4. IV.5 ГѴ.6 Nonhomogeneous linear systems Weakly nonlinear equations—noncritical case The general saddle point property More general systems The Duffing equation with large damping and large forcing Remarks and extensions 144 145 154 156 162 168 171 CHAPTER V. Simple oscillatory phenomena and the method of averaging V.l. V.2. V.3. V.4. V.5. Conservative systems Nonconservative second order equations—limitcycles Averaging The forced van der Pol equation Duffing’s equation with small damping and small harmonic forcing V.6. The subharmonic of order 3 for Duffing’s equation V.7. Damped excited pendulum with oscillating support V.8. Exercises V.9. Remarks and suggestions for further study 175 176 184 190 198 199 206 208 210 211 CHAPTER VI. Behavior near a periodic orbit VI.1. A local coordinate system about an invariant closed curve 213 214
VI.2. Stability of a periodic orbit VI.3. Sufficient conditions for orbital stability in two dimensions VI.4. Autonomous perturbations VI.5. Remarks and suggestions for further study 219 224 225 227 CHAPTER VII. Integral manifolds of equations with a small parameter VILI. VII.2. VII.3. VII.4. VII.6. VII.6. VII.7. VII.8. VII.9. Methods of determining integral manifolds Statement of results A “nonhomogeneous linear ” system The mapping principle Proof of Theorem 2.1 Stability of the perturbed manifold Applications Exercises Remarks and suggestions for further study 229 231 236 239 245 247 248 250 254 256 CHAPTER VIII. Periodic systems with a small parameter VIILI. VIII.2. VIII.3. VIII.4. A special system of equations Almost linear systems Periodic solutions of perturbed autonomous equations Remarks and suggestions for further study 258 259 275 294 296 CHAPTER IX. Alternative problems for the solution of functional equations IX. 1. IX.2. IX.3. IX.4. IX.5. IX.6. Equivalent equations A generalization Alternative problems Alternative.problems for periodic solutions The Perron-Lettenmeyer theorem Remarks and suggestions for further study 298 299 302 303 304 307 309
CHAPTER X. The direct method of Liapunov X.l. X.2. X.3. X.4. X.6. X.6. X.7. Sufficient conditions for stability and instability in autonomous systems Circuits containing Esaki diodes Sufficient conditions for stability in nonautonomous systems The converse theorems for asymptotio stability Implications of asymptotic stability Wazewski’s principle Remarks and suggestions for further study 311 311 320 324 327 331 333 338 APPENDIX Almost periodic functions References Index 339 351 359
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| any_adam_object | 1 |
| author | Hale, Jack K. 1928-2009 |
| author_GND | (DE-588)172122503 |
| author_facet | Hale, Jack K. 1928-2009 |
| author_role | aut |
| author_sort | Hale, Jack K. 1928-2009 |
| author_variant | j k h jk jkh |
| building | Verbundindex |
| bvnumber | BV035691762 |
| classification_rvk | SK 520 |
| classification_tum | MAT 340f |
| ctrlnum | (OCoLC)294885198 (DE-599)BVBBV035691762 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | unabridged republ. of the work orig. publ. ... New York: Wiley, 1969 |
| format | Book |
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| id | DE-604.BV035691762 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:32Z |
| institution | BVB |
| isbn | 9780486472119 0486472116 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017745831 |
| oclc_num | 294885198 |
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| physical | XIV, 361 S. Ill. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Dover Publ. |
| record_format | marc |
| spelling | Hale, Jack K. 1928-2009 Verfasser (DE-588)172122503 aut Ordinary differential equations Jack K. Hale unabridged republ. of the work orig. publ. ... New York: Wiley, 1969 Mineola, N.Y. Dover Publ. 2009 XIV, 361 S. Ill. txt rdacontent n rdamedia nc rdacarrier Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Differentialgleichung (DE-588)4012249-9 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017745831&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hale, Jack K. 1928-2009 Ordinary differential equations Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4020929-5 |
| title | Ordinary differential equations |
| title_auth | Ordinary differential equations |
| title_exact_search | Ordinary differential equations |
| title_full | Ordinary differential equations Jack K. Hale |
| title_fullStr | Ordinary differential equations Jack K. Hale |
| title_full_unstemmed | Ordinary differential equations Jack K. Hale |
| title_short | Ordinary differential equations |
| title_sort | ordinary differential equations |
| topic | Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Differentialgleichung Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017745831&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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