Elementary differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Macmillan [u.a.]
1974
|
| Edition: | 5. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Chaper 1 - 16 of this book [also] appear seperately as "A short course in differential equations, 5. ed." Some material is from "Laplace transforms : an introduction" / by Earl D. Rainville. - 1963 |
| Physical Description: | XIII, 511 S. graph. Darst. |
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MARC
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| 100 | 1 | |a Rainville, Earl David |d 1907-1966 |e Verfasser |0 (DE-588)172324386 |4 aut | |
| 245 | 1 | 0 | |a Elementary differential equations |c Earl D. Rainville ; Phillip E. Bedient* |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Macmillan [u.a.] |c 1974 | |
| 300 | |a XIII, 511 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Chaper 1 - 16 of this book [also] appear seperately as "A short course in differential equations, 5. ed." | ||
| 500 | |a Some material is from "Laplace transforms : an introduction" / by Earl D. Rainville. - 1963 | ||
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Differential equations | |
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Record in the Search Index
| _version_ | 1804117337071157248 |
|---|---|
| adam_text | Contents
1 Definitions, Elimination of Arbitrary Constants
1. Examples of differential equations 1
2. Definitions 3
3. The elimination of arbitrary constants 5
4. Families of curves 9
2 Equations of Order One
5. The isoclines of an equation 16
6. An existence theorem 19
7. Separation of variables 20
8. Homogeneous functions 25
9. Equations with homogeneous coefficients 27
10. Exact equations 30
11. The linear equation of order one 35
vii
viii Contents
12. The general solution of a linear equation 39
Miscellaneous exercises 41
3 Elementary Applications
13. Velocity of escape from the earth 45
14. Newton s law of cooling 47
15. Simple chemical conversion 48
16. Orthogonal trajectories; rectangular coordinates 53
17. Orthogonal trajectories; polar coordinates 56
4 Additional Topics on Equations of Order One
18. Integrating factors found by inspection 59
19. The determination of integrating factors 63
20. Substitution suggested by the equation 68
21. Bernoulli s equation 70
22. Coefficients linear in the two variables 73
23. Solutions involving nonelementary integrals 78
Miscellaneous exercises 80
5 Linear Differential Equations
24. The general linear equation 82
25. Linear independence 83
26. An existence and uniqueness theorem 84
27. TheWronskian 84
28. General solution of a homogeneous equation 87
29. General solution of a nonhomogeneous equation 89
30. Differential operators 90
31. The fundamental laws of operation 93
32. Some properties of differential operators 94
6 Linear Equations with Constant Coefficients
33. Introduction 98
34. The auxiliary equation; distinct roots 98
35. The auxiliary equation; repeated roots 101
36. A definition of exp z for imaginary z 105
Contents ix
37. The auxiliary equation; imaginary roots 106
Miscellaneous exercises 109
7 Nonhomogeneous Equations: Undetermined Coefficients
38. Construction of a homogeneous equation from a specified
solution 111
39. Solution of a nonhomogeneous equation 114
40. The method of undetermined coefficients 116
41. Solution by inspection 122
8 Variation of Parameters
42. Introduction 127
43. Reduction of order 128
44. Variation of parameters 132
45. Solution of/ + y = f(x) 136
Miscellaneous exercises 139
9 Inverse Differential Operators
46. The exponential shift 140
47. The operator 1//(D) 144
48. Evaluation of [1//(/))] e°x 145
49. Evaluation of (D2 + a2) sin ax and (D2 + a2)~l cos ax 146
10 The Laplace Transform
50. The transform concept 150
51. Definition of the Laplace transform 151
52. Transforms of elementary functions 152
53. Transforming initial value problems 156
54. Sectionally continuous functions 159
55. Functions of exponential order 161
56. Functions of class A 164
57. Transforms of derivatives 166
58. Derivatives of transforms 169
59. The gamma function 170
60. Periodic functions 171
x Contents
11 Inverse Transforms
61. Definition of an inverse transform 177
62. A step function 181
63. A convolution theorem 186
64. Simple initial value problems 190
65. Special integral equations 197
12 Applications
66. Vibration of a spring 204
67. Undamped vibrations 207
68. Resonance 211
69. Damped vibrations 213
70. The simple pendulum and the deflection of beams 218
13 Systems of Equations
71. Introduction 225
72. Elementary elimination calculus 225
73. First order systems with constant coefficients 229
74. Solution of a first order system 231
75. Some matrix algebra 232
76. First order systems revisited 239
77. Complex eigenvalues 246
78. Repeated eigenvalues 251
79. Nonhomogeneous systems 257
80. The Laplace transform 260
14 Electric Circuits and Networks
81. Circuits 266
82. Simple networks 269
15 The Existence and Uniqueness of Solutions
83. Preliminary remarks 279
84. An existence and uniqueness theorem 280
85. A Lipschitz condition 282
Contents xi
86. A proof of the existence theorem 283
87. A proof of the uniqueness theorem 286
88. Other existence theorems 288
16 Nonlinear Equations
89. Preliminary remarks 289
90. Factoring the left member 290
91. Singular solutions 293
92. The odiscriminant equation 294
93. The /7 discriminant equation 296
94. Eliminating the dependent variable 298
95. Clairaut s equation 300
96. Dependent variable missing 303
97. Independent variable missing 305
98. The catenary 308
Miscellaneous exercises 310
17 Power Series Solutions
99. Linear equations and power series 312
100. Convergence of power series 314
101. Ordinary points and singular points 316
102. Validity of the solutions near an ordinary point 317
103. Solutions near an ordinary point 318
18 Solutions Near Regular Singular Points
104. Regular singular points 329
105. The indicial equation 332
106. Form and validity of the solutions near a regular singular point 334
107. Indicial equation with difference of roots nonintegral 334
108. Differentiation of a product of functions 340
109. Indicial equation with equal roots 341
110. Indicial equation with difference of roots a positive integer,
nonlogarithmic case 348
111. Indicial equation with difference of roots a positive integer,
logarithmic case 352
112. Solution for large x 357
113. Many term recurrence relations 362
xii Contents
114. Summary 366
Miscellaneous exercises 368
19 Equations of Hypergeometric Type
115. Equations to be treated in this chapter 370
116. The factorial function 370
117. The hypergeometric equation 371
118. Laguerre polynomials 373
119. Bessel s equation with index not an integer 374
120. Bessel s equation with index an integer 375
121. Hermite polynomials 377
122. Legendre polynomials 377
123. The confluent hypergeometric equation 379
20 Numerical Methods
124. General remarks 381
125. The increment method 382
126. A method of successive approximation 384
127. An improvement on the preceding method 386
128. The use of Taylor s theorem 387
129. The Runge Kutta method 389
130. A continuing method 392
21 Partial Differential Equations
131. Remarks on partial differential equations 396
132. Some partial differential equations of applied mathematics 397
133. Method of separation of variables 399
134. A problem on the conduction of heat in a slab 404
22 Orthogonal Sets
135. Orthogonality 410
136. Simple sets of polynomials 411
137. Orthogonal polynomials 412
138. Zeros of orthogonal polynomials 413
139. Orthogonality of Legendre polynomials 414
140. Other orthogonal sets 416
Contents xiii
23 Fourier Series
141. Orthogonality of a set of sines and cosines 418
142. Fourier series: an expansion theorem 421
143. Numerical examples of Fourier series 425
144. Fourier sine series 434
145. Fourier cosine series 438
146. Numerical Fourier analysis 442
147. Improvement in rapidity of convergence 443
24 Boundary Value Problems
148. The one dimensional heat equation 445
149. Experimental verification of the validity of the heat equation 451
150. Surface temperature varying with time 454
151. Heat conduction in a sphere 456
152. The simple wave equation 458
153. Laplace s equation in two dimensions 461
25 Additional Properties of the Laplace Transform
154. Power series and inverse transforms 465
155. The error function 469
156. Bessel functions 476
157. Differential equations with variable coefficients 479
26 Partial Differential Equations; Transform Methods
158. Boundary value problems 480
159. The wave equation 485
160. Diffusion in a semi infinite solid 487
161. Canonical variables 490
162. Diffusion in a slab of finite width 492
163. Diffusion in a quarter infinite solid 496
Index 501
|
| any_adam_object | 1 |
| author | Rainville, Earl David 1907-1966 Bedient, Phillip Edward 1922- |
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| edition | 5. ed. |
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| language | English |
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| physical | XIII, 511 S. graph. Darst. |
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| spelling | Rainville, Earl David 1907-1966 Verfasser (DE-588)172324386 aut Elementary differential equations Earl D. Rainville ; Phillip E. Bedient* 5. ed. New York [u.a.] Macmillan [u.a.] 1974 XIII, 511 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaper 1 - 16 of this book [also] appear seperately as "A short course in differential equations, 5. ed." Some material is from "Laplace transforms : an introduction" / by Earl D. Rainville. - 1963 Équations différentielles Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Differentialgleichung (DE-588)4012249-9 s DE-604 Bedient, Phillip Edward 1922- Verfasser (DE-588)171970276 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001909872&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 | Rainville, Earl David 1907-1966 Bedient, Phillip Edward 1922- Elementary differential equations Équations différentielles Differential equations Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4143389-0 |
| title | Elementary differential equations |
| title_auth | Elementary differential equations |
| title_exact_search | Elementary differential equations |
| title_full | Elementary differential equations Earl D. Rainville ; Phillip E. Bedient* |
| title_fullStr | Elementary differential equations Earl D. Rainville ; Phillip E. Bedient* |
| title_full_unstemmed | Elementary differential equations Earl D. Rainville ; Phillip E. Bedient* |
| title_short | Elementary differential equations |
| title_sort | elementary differential equations |
| topic | Équations différentielles Differential equations Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Équations différentielles Differential equations Differentialgleichung Aufgabensammlung |
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