Elements of ordinary differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
MacGraw-Hill
1965
|
| Edition: | 2. ed. |
| Series: | International series in pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 410 S. graph. Darst. |
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MARC
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| 245 | 1 | 0 | |a Elements of ordinary differential equations |c Michael Golomb ; Merrill Shanks |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b MacGraw-Hill |c 1965 | |
| 300 | |a XI, 410 S. |b graph. Darst. | ||
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| 490 | 0 | |a International series in pure and applied mathematics | |
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Record in the Search Index
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| adam_text | Contents
Preface v
I Some Basic Facts and Techniques 1
1. Differential Equations Defined 1
2. Solution or Integral of a Differential Equation 3
3. Solution by Quadrature 7
4. Solution by Separation of Variables 11
5. Direction Fields 14
6. Numerical Methods 18
7. Round off Errors 33
8. The Method of Successive Approximations 35
II Techniques for Solving First order Equations 39
1. Linear Equations 40
2. Exact Equations 44
3. Integrating Factors 52
4. Change of Variables 56
III Existence, Uniqueness, and Geometry of Solutions 63
1. A Basic Inequality 63
2. Convergence of Approximate Solutions; Uniqueness 65
3. Convergence of Numerical Methods; Existence 70
IV Applications of First order Equations 81
A. Curves 82
1. Differential Equations of Curves 82
2. Orthogonal Trajectories 87
ix
x CONTENTS
3. Clairaut s Equation; Envelopes 92
4. The General First order Equation 98
B. Growth, Decay, Change 100
5. Rate Problems 100
C. Flows 105
6. Problems of Fluid Flow 105
7. Problems of Heat Flow 108
8. Some Thermodynamic Relations 110
D. Motions 113
9. Newton s Second Law 113
10. The Pendulum 118
11. Planetary and Satellite Motion 123
E. Circuits 126
12. Simple Circuits 126
13. Nonlinear Circuits 132
V Second order Differential Equations 134
1. Some Simple Classes of Second order Equations 134
2. Linear Equations with Constant Coefficients 138
3. Complex Roots 143
4. The Nonhomogeneous Equation 146
5. The Method of Undetermined Coefficients 148
6. The Method of Variation of Parameters 151
7. Oscillatory Systems 156
8. The Superposition Principle 157
9. Free Vibrations 158
10. Simple Forcing Functions 161
11. Superposition of Simple Solutions 164
12. Connection with Systems; Existence and Uniqueness 166
13. Numerical Solutions 169
14. Boundary value Problems 174
15. Static equilibrium Problems 179
16. Some Dynamic Problems 186
VI Linear Differential Equations of Higher Order;
Constant Coefficients 191
1. Linear Operators 191
2. Existence and Uniqueness of Solutions 194
3. Linear Combinations and Linear Independence 198
4. Vector Spaces 201
5. General Solution of the Homogeneous Equation 205
6. Constant Coefficients; Differential Operators 209
7. Application to the Solution of Homogeneous Equations 212
8. The General Nonhomogeneous Equation 218
9. Principle of Superposition 222
10. Nonhomogeneous, Constant Coefficients 224
CONTENTS X|
11. Method 1: Successive Integrations 224
12. Method 2: Undetermined Coefficients 226
13. Method 3: Reduction to Method 2 229
14. Method 4: Green s Functions 232
VII Laplace Transforms and Operator Methods 245
1. The Laplace Transform 245
2. Some Theorems on Transforms 249
3. Application to Differential Equations with Constant
Coefficients 255
4. Convolutions 258
5. The 8 Function and Green s Function 261
6. Steady State; Stability 264
7. Inverse Operators 267
8. Comparison of Operator and Transform Methods 274
VIII Systems of Differential Equations 276
1. Systems of Simultaneous Linear Differential Equations 276
2. Reduction to Triangular Form 282
3. The Laplace transform Method 288
4. Special Systems; Existence and Uniqueness 293
5. Applications to Mechanical Systems 303
6. Applications to Electrical Systems 308
IX Linear Equations with Variable Coefficients 312
1. Equations of Euler Cauchy 313
2. Reduction by Known Integrals 316
3. Method of Variation of Parameters 319
4. Transformation of Variables 322
5. Removal of the Second Highest Derivative 326
6. Exact Differential Equations and Integrating Factors 328
7. Equations of Riccati 332
8. Periodic Coefficients; Periodic Solutions 336
X Solution in Power Series; Some Classical Equations 340
1. Analytic Functions 340
2. Ordinary Points 344
3. The Method of Undetermined Coefficients; Ordinary Points 346
4. Regular Singular Points 351
5. Bessel s Differential Equation 358
6. Gauss s Hypergeometric Equation 362
7. Roots of Indicial Equation Differing by an Integer 365
8. The Point at Infinity 369
9. Legendre s Differential Equation 373
References 379
Answers 381
Index 407
|
| any_adam_object | 1 |
| author | Golomb, Michael 1909- Shanks, Merrill 1911- |
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| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.38 |
| dewey-search | 517.38 |
| dewey-sort | 3517.38 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:56:03Z |
| institution | BVB |
| language | English |
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| physical | XI, 410 S. graph. Darst. |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | MacGraw-Hill |
| record_format | marc |
| series2 | International series in pure and applied mathematics |
| spelling | Golomb, Michael 1909- Verfasser (DE-588)12562526X aut Elements of ordinary differential equations Michael Golomb ; Merrill Shanks 2. ed. New York MacGraw-Hill 1965 XI, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Ecuaciones diferenciales 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 DE-604 Differentialgleichung (DE-588)4012249-9 s Shanks, Merrill 1911- Verfasser (DE-588)132734648 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004541252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golomb, Michael 1909- Shanks, Merrill 1911- Elements of ordinary differential equations Ecuaciones diferenciales 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 | Elements of ordinary differential equations |
| title_auth | Elements of ordinary differential equations |
| title_exact_search | Elements of ordinary differential equations |
| title_full | Elements of ordinary differential equations Michael Golomb ; Merrill Shanks |
| title_fullStr | Elements of ordinary differential equations Michael Golomb ; Merrill Shanks |
| title_full_unstemmed | Elements of ordinary differential equations Michael Golomb ; Merrill Shanks |
| title_short | Elements of ordinary differential equations |
| title_sort | elements of ordinary differential equations |
| topic | Ecuaciones diferenciales Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Ecuaciones diferenciales Differential equations Differentialgleichung Gewöhnliche Differentialgleichung |
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