Holdings: Calculus of finite differences

Calculus of finite differences:

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Bibliographic Details
Main Author:	Jordan, Charles (Author)
Format:	Book
Language:	English
Published:	New York, NY Chelsea Publ. Co. 1965
Edition:	3. ed.
Subjects:	Difference equations Interpolation Differenzenrechnung Differenzengleichung Numerisches Verfahren Differentialgleichung
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 654 S. graph. Darst.

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MARC


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245	1	0	\|a Calculus of finite differences \|c by Charles Jordan
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Record in the Search Index

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adam_text	CONTENTS. Chapter I. On Operations. § 1. Historical and Bibliographical Notes .... 1 § 2. Definition of differences 2 § 3. Operation of displacement 5 § 4. Operation of the mean 6 § 5. Symbolical Calculus 7 § 6. Symbolical methods 8 § 7. Receding Differences 14 § 8. Central Differences 15 § 9. Divided Differences 18 § 10. Generating functions 20 § 11. General rules to determine generating functions . 25 § 12. Expansion of functions into power series ... 29 § 13. Expansion of function by aid of decomposition into partial fractions 34 § 14. Expansion of functions by aid of complex integrals . 40 § 15. Expansion of a function by aid of difference equations 41 Chapter II. Functions important in the Calculus of Finite Differences. § 16. The Factorial 45 § 17. The Gamma function 53 § 18. Incomplete Gamma function 56 § 19. The Digamma function 58 § 20. The Trigamma function 60 § 21. Expansion of logr(x M) into a power series . . 61 § 22. The Binomial coefficient • 62 § 23. Expansion of a function into a series of binomial coefficients xii § 24. Beta functions 80 § 25. Incomplete Beta functions 83 § 26. Exponential functions 87 § 27. Trigonometric functions 88 § 28. Alternate functions 92 § 29. Functions whose differences or means are equal to zero 94 § 30. Product of two functions. Differences .... 94 § 31. Product of two functions. Means 98 Chapter 111. Inverse Operation of Differences and Means. Sums. § 32. Indefinite sums 100 § 33. Indefinite sum obtained by inversion .... 103 § 34. Indefinite sum obtained by summation by parts . . 105 § 35. Summation by parts of alternate functions . . .108 § 36. Indefinite sums determined by difference equations . 109 § 37. Differences, sums and means of infinite series . , 110 § 38. Inverse operation of the mean Ill § 39. Other methods of obtaining inverse means . . ,113 § 40. Sums 116 § 41. Sums determined by indefinite sums 117 § 42. Sum of reciprocal factorials by indefinite sums . . 121 § 43. Sums of exponential and trigonometric functions . 123 § 44. Sums of other Functions 129 § 45. Determination of sums by symbolical formulae . . 131 § 46. Determination of sums by generating functions . .136 § 47. Determination of sums by geometrical considerations 138 § 48. Determination of sums by the Calculus of Probability 140 § 49. Determination of alternate sums starting from usual sums 140 Chapter IV. Stirling s Numbers. § 50. Expansion of factorials into power series. Stirling s numbers of the first kind 142 § 51. Determination of the Stirling numbers starting from their definition 145 § 52. Resolution of the difference equations . . . .147 xiii § 53. Transformation of a multiple sum without repeti¬ tion into sums without restriction 153 § 54. Stirling s numbers expressed by sums. Limits . . 159 § 55. Application of the Stirling numbers of the first kind 163 § 56. Derivatives expressed by differences . . . .164 § 57. Stirling numbers of the first kind obtained by proba¬ bility 166 § 58. Stirling numbers of the second kind 168 § 59. Limits of expressions containing Stirling numbers of the second kind 173 § 60. Generating functions of the Stirling numbers of the second kind 174 § 61. Stirling numbers of the second kind obtained by probability 177 § 62. Decomposition of products of prime numbers into factors 179 § 63. Application of the expansion of powers into series of factorials 181 § 64. Formulae containing Stirling numbers of both kinds 182 § 65. Inversion of sums and series. Sum equations . . 183 § 66. Deduction of certain formulae containing Stirling numbers 185 § 67. Differences expressed by derivatives .... 189 § 68. Expansion of a reciprocal factorial into a series of reciprocal powers and vice versa 192 § 69. The operation 0 195 § 70. The operation W 199 § 71. Operations AmD m and DmA m 200 § 72. Expansion of a function of function by aid of Stirling numbers. Semi invariants of Thiele 204 § 73. Expansion of a function into reciprocal factorial series and into reciprocal power series .... 212 § 74. Expansion of the function 1/y into a series of powers of x 216 § 75. Changing the origin of the intervals 219 § 76. Changing the length of the interval 220 § 77. Stirling s polynomials 224 xiv Chapter V. Bernoulli Polynomials and Numbers. § 78. Bernoulli polynomials of the first kind .... 230 § 79. Particular cases of the Bernoulli polynomials . . 236 § 80. Symmetry of the Bernoulli polynomials .... 238 § 81. Operations performed on the Bernoulli polynomial . 240 § 82. Expansion of the Bernoulli polynomial into a Fourier series. Limits. Sum of reciprocal power series . . 242 § 83. Application of the Bernoulli polynomials . . . 246 § 84. Expansion of a polynomial into Bernoulli polynomials 248 § 85. Expansion of functions into Bernoulli polynomials. Generating functions 250 § 86. Raabe s multiplication theorem of the Bernoulli polynomials 252 § 87. The Bernoulli series 253 § 88. The Maclaurin Euler summation formula . . . 260 § 89. Bernoulli polynomials of the second kind . . . 265 § 90. Symmetry of the Bernoulli polynomials of the second kind 268 § 91. Extrema of the polynomials 269 § 92. Particular cases of the polynomials .... 272 § 93. Limits of the numbers bn and of the polynomials yn [x] 272 § 94. Operations on the Bernoulli polynomials of the second kind 275 § 95. Expansion of the Bernoulli polynomials of the second kind 276 § 96. Application of the polynomials 277 § 97. Expansion of a polynomial into a series of Bernoulli polynomials of the second kind 277 § 98. The Bernoulli series of the second kind .... 280 § 99. Gregory s summation formula 284 Chapter VI. Euler s and Boole s polynomials. Sums of reciprocal powers. § 100. Euler s polynomials 288 § 101. Symmetry of the Euler polynomials .... 292 § 102. Expansion of the Euler polynomials into a series of Bernoulli polynomials of the first kind . . . 295 XV § 103. Operations on the Euler polynomials .... 296 § 104. The Tangent coefficients 298 § 105. Euler numbers 300 § 106. Limits of the Euler polynomials and numbers . . 302 § 107. Expansion of the Euler polynomials into Fourier series 303 § 108. Application of the Euler polynomials .... 306 § 109. Expansion of a polynomial into a series of Euler polynomials 307 § 110. Multiplication theorem of the Euler polynomials . 311 § 111. Expansion of a function into an Euler series . . 313 § 112. Boole s first summation formula 315 § 113. Boole s polynomials 317 § 114. Operations on the Boole polynomials. Differences . 320 § 115. Expansion of the Boole polynomials into a series of Bernoulli polynomials of the second kind . . . 321 § 116. Expansion of a function into Boole polynomials . 322 § 117. Boole s second summation formula 323 § 118. Sums of reciprocal powers. Sum of 1/x by aid of the digamma function 325 § 119. Sum of 1/x2 by aid of the trigamma function . . 330 § 120. Sum of a rational fraction 335 § 121. Sum of reciprocal powers. Sum of xm .... 338 § 122. Sum of alternate reciprocal powers by the /M) function 347 Chapter VII. Expansion of Functions, Interpolation, Construction of Tables. § 123. Expansion of a Function into a series of polynomials 355 § 124. The Newton series 357 § 125. Interpolation by aid of Newton s Formula and Construction of Tables 360 § 126. Inverse interpolation by Newton s formula . . 366 § 127. Interpolation by the Gauss series 368 § 128. The Bessel and the Stirling series 373 § 129. Everett s formula 376 § 130. Inverse interpolation by Everett s formula . . 381 § 131. Lagrange s interpolation formula 385 xvi § 132. Interpolation formula without printed differences. Remarks on the construction of tables .... 390 § 133. Inverse Interpolation by aid of the formula of the preceding paragraph 411 § 134. Precision of the interpolation formulae . . . .417 § 135. General Problem of Interpolation 420 Chapter VIII. Approximation and Graduation. § 136. Approximation according to the principle of moments 422 § 137. Examples of function chosen 426 § 138. Expansion of a Function into a series of Legendre s polynomials 434 § 139. Orthogonal polynomials with respect to x=jc0, ! **¦_! 426 § 140. Mathematical properties of the orthogonal poly¬ nomials 442 § 141. Expansion of a function into a series of orthogonal polynomials 447 § 142. Approximation of a function given for i—0,1, 2, . .. , N—l 451 § 143. Graduation by the method of least squares . . 456 § 144. Computation of the binomial moments .... 460 § 145. Fourier series 463 § 146. Approximation by trigonometric functions of dis¬ continuous variables 465 § 147. Hermite polynomials 467 § 148. G. polynomials 473 Chapter IX. Numerical resolution of equations. Numerical integration. § 149. Method of False Position. Regula Falsi ... 486 § 150. The Newton Raphson method 489 § 151. Method of Iteration 492 § 152. Daniel Bernoulli s method 494 § 153. The Ch in Vieta Horner method 496 § 154. Root squaring method. Dandelin, Lobatchevsky, Graeffe 503 xvii § 155. Numerical Integration 512 § 156. Hardy and Weddle s formulae 516 § 157. The Gauss Legendre method 517 § 158. Tchebichef s formula 519 § 159. Numerical integration of functions expanded into a series of their differences 524 § 160. Numerical resolution of differential equations . . 527 Chapter X. Functions of several independent variables. § 161. Functions of two variables 530 § 162. Interpolation in a double entry table .... 532 § 163. Functions of three variables 541 Chapter XI. Difference Equations. § 164. Genesis of difference equations 543 § 165. Homogeneous linear difference equations, constant coefficients 545 § 166. Characteristic equations with multiple roots . . 549 § 167. Negative roots 552 § 168. Complex roots 554 § 169. Complete linear equations of differences with constant coefficients 557 § 170. Determination of the particular solution in the general case 564 § 171. Method of the arbitrary constants 569 § 172. Resolution of linear equations of differences by aid of generating functions 572 § 173. Homogeneous linear equations of the first order with variable coefficients 576 § 174. Laplace s method for solving linear homogeneous difference equations with variable coefficients . . 579 § 175. Complete linear equations of differences of the first order with variable coefficients 583 § 176. Reducible linear equations of differences with va¬ riable coefficients 584 § 177. Linear equations of differences whose coefficients are polynomials of x, solved by the method of generating functions oo° xviii § 178. Andre s method for solving difference equations . 587 § 179. Sum equations which are reducible to equations of differences 599 § 180. Simultaneous linear equations of differences with constant coefficients 600 Chapter XIII. Equations of Partial Differences. § 181. Introduction 604 § 182. Resolution of linear equations of partial differences with constant coefficients by Laplace s method of generating functions 607 § 183. Boole s symbolical method for solving equations of partial differences 616 § 184. Method of Fourier, Lagrange, and Ellis for solving equations of partial differences 619 § 185. Homogeneous linear equations of mixed differences 632 § 186. Difference equations of three independent variables 633 § 187. Differences equations of four independent variables 638
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discipline	Mathematik Wirtschaftswissenschaften
edition	3. ed.
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spelling	Jordan, Charles Verfasser aut Calculus of finite differences by Charles Jordan 3. ed. New York, NY Chelsea Publ. Co. 1965 XXI, 654 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Difference equations Interpolation Interpolation (DE-588)4162121-9 gnd rswk-swf Differenzenrechnung (DE-588)4149800-8 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differenzenrechnung (DE-588)4149800-8 s DE-604 Differenzengleichung (DE-588)4012264-5 s Numerisches Verfahren (DE-588)4128130-5 s Differentialgleichung (DE-588)4012249-9 s Interpolation (DE-588)4162121-9 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=001755366&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	Jordan, Charles Calculus of finite differences Difference equations Interpolation Interpolation (DE-588)4162121-9 gnd Differenzenrechnung (DE-588)4149800-8 gnd Differenzengleichung (DE-588)4012264-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd
subject_GND	(DE-588)4162121-9 (DE-588)4149800-8 (DE-588)4012264-5 (DE-588)4128130-5 (DE-588)4012249-9
title	Calculus of finite differences
title_auth	Calculus of finite differences
title_exact_search	Calculus of finite differences
title_full	Calculus of finite differences by Charles Jordan
title_fullStr	Calculus of finite differences by Charles Jordan
title_full_unstemmed	Calculus of finite differences by Charles Jordan
title_short	Calculus of finite differences
title_sort	calculus of finite differences
topic	Difference equations Interpolation Interpolation (DE-588)4162121-9 gnd Differenzenrechnung (DE-588)4149800-8 gnd Differenzengleichung (DE-588)4012264-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd
topic_facet	Difference equations Interpolation Differenzenrechnung Differenzengleichung Numerisches Verfahren Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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