Ordinary differential equations and their solutions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
VanNostrand
1960
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 451 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Ordinary differential equations and their solutions |c by George M. Murphy |
| 264 | 1 | |a Princeton, NJ |b VanNostrand |c 1960 | |
| 300 | |a IX, 451 S. | ||
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| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804116680061747200 |
|---|---|
| adam_text | CONTENTS
Preface iii
Introduction 1
PART I. METHODS FOR SOLVING ORDINARY
DIFFERENTIAL EQUATIONS 7
A. The Differential Equation Is of First Order 8
Al. The Equation Is of First Order and of First Degree 9
1. Separable Variables 10
2. The Linear Equation 13
3. The Riccati Equation 15
4. The Abel Equation 23
5. The Bernoulli Equation 26
6. Equations Linear in the Variables 27
7. The Exact Equation and the Integrating Factor 28
8. Homogeneous Equations and Related Types 34
9. Change of Variable 40
10. The General Equation of First Order and First Degree 43
11. Series Solution 46
12. Solution as an Integral Equation 53
13. Approximate Methods 54
A2. The Equation Is of First Order and of Second or Higher Degree 58
1. Missing Variables 59
2. No Missing Variables 61
3. Homogeneous Equations and Related Types 63
4. Clairaut s Equation and Related Types 65
5. The Method of Lagrange 66
6. Change of Variable 66
7. The General Equation 67
8. X0(x,y)pm + Xl(x,y)pm 1 + ... + Xm(x,y) = 0 68
9. vm +fi(.*,y)Pm~1 + +fn, i(x,y)p+fm(x,y) = 0 70
10. Singular Solutions 74
11. The Equation Is Transcendental in dy/dx 80
vii
viii CONTENTS
B. The Differential Equation Is of Second Order 81
Bl. The Linear Equation of Second Order 82
1. The Linear Homogeneous Equation with Constant
Coefficients 84
2. The Linear Homogeneous Equation with Variable
Coefficients 85
3. Equations Reducible to Type 1 86
4. Transformations of the Linear Equation 87
5. The Exact Equation 92
6. Resolution of Operators 94
7. Solution of the Equation in Infinite Form 95
8. Series Solution 96
9. Equations of Standard Type 108
10. Integral Solution 138
11. Continued Fraction Solution 144
12. The Linear Nonhomogeneous Equation 145
B2. The Nonlinear Equation of Second Order 158
1. The Dependent Variable Is Missing 158
2. The Independent Variable Is Missing 159
3. Homogeneous Equations 161
4. The Exact Nonlinear Equation 164
5. Change of Variable 166
6. The General Nonlinear Equation of Second Order 166
7. The Equation with Fixed Critical Points 166
8. The Equation with Fixed Critical Points, Rational in y 168
9. Painleve Equations 183
10. The Equation with Fixed Critical Points, Algebraic in y 185
11. Singular Solutions 186
C. The Differential Equation Is of Order Greater Than Two 188
Cl. The Linear Equation of Order Greater Than Two 190
1. The Linear Homogeneous Equation with Constant
Coefficients 191
2. The Linear Homogeneous Equation with Variable
Coefficients 192
3. Equations Reducible to Type 1 193
4. Transformations of the Equation 194
5. The Exact Equation 196
6. Series Solution 200
7. Fuchsian Equations and Others with Special Properties 210
CONTENTS ix
8. Integral Solutions 213
9. The Linear Nonhomogeneous Equation 215
C2. The Nonlinear Equation of Order Greater Than Two 217
1. The Dependent Variable Is Missing 217
2. The Independent Variable Is Missing 218
3. Homogeneous Equations 220
4. The Exact Nonlinear Equation 221
5. Other Procedures 222
PART II. TABLES OF DIFFERENTIAL EQUATIONS AND
THEIR SOLUTIONS 223
1. The Differential Equation Is of First Order and of First Degree 224
2. The Differential Equation Is of First Order and of Second or Higher
Degree 278
3. The Differential Equation Is Linear and of Second Order 311
4. The Nonlinear Equation of Second Order 380
5. The Equation Is Linear and of Order Greater than Two 410
6. The Equation Is Nonlinear and of Order Greater than Two 427
Index of Equation Types 431
Bibliography 436
Index 443
|
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| indexdate | 2024-07-09T15:42:21Z |
| institution | BVB |
| language | English |
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| physical | IX, 451 S. |
| publishDate | 1960 |
| publishDateSearch | 1960 |
| publishDateSort | 1960 |
| publisher | VanNostrand |
| record_format | marc |
| spelling | Murphy, George Moseley Verfasser aut Ordinary differential equations and their solutions by George M. Murphy Princeton, NJ VanNostrand 1960 IX, 451 S. txt rdacontent n rdamedia nc rdacarrier Gewone differentiaalvergelijkingen gtt Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001462003&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 | Murphy, George Moseley Ordinary differential equations and their solutions Gewone differentiaalvergelijkingen gtt Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4012249-9 |
| title | Ordinary differential equations and their solutions |
| title_auth | Ordinary differential equations and their solutions |
| title_exact_search | Ordinary differential equations and their solutions |
| title_full | Ordinary differential equations and their solutions by George M. Murphy |
| title_fullStr | Ordinary differential equations and their solutions by George M. Murphy |
| title_full_unstemmed | Ordinary differential equations and their solutions by George M. Murphy |
| title_short | Ordinary differential equations and their solutions |
| title_sort | ordinary differential equations and their solutions |
| topic | Gewone differentiaalvergelijkingen gtt Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Gewone differentiaalvergelijkingen Differential equations Gewöhnliche Differentialgleichung Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001462003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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