Introduction to numerical analysis using MATLAB / (Record no. 521)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 12837cam a2200217 a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 1776 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200702105427.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 070508s2010 maua b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781934015230 (hardcover with CDROM : alk. paper) |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | DLC |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 518 |
| Edition number | 22 |
| Item number | B9881 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Butt, Rizwan. |
| 245 10 - TITLE STATEMENT | |
| Title | Introduction to numerical analysis using MATLAB / |
| Statement of responsibility, etc | Rizwan Butt. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Sudbury, Mass. : |
| Name of publisher, distributor, etc | Jones and Bartlett Publishers, |
| Date of publication, distribution, etc | c2010. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xv, 814 p. |
| Other physical details | ill. ; |
| Dimensions | 25 cm. + |
| Accompanying material | 1CD-ROM (4 3/4 in.). |
| 490 0# - SERIES STATEMENT | |
| Series statement | Mathematics series |
| 500 ## - GENERAL NOTE | |
| General note | Includes bibliographical references (p. 801-808) and index. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numerical analysis |
| General subdivision | Data processing. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Books |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Contents<br/>2. 1 Number Systems and Errors 1<br/>3. 1.1 <br/>4. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br/>5. 1.2 <br/>6. Number Representation and Base of Numbers . . . . . . . . . . . . . 2<br/>7. 1.2.1 <br/>8. Normalized Floating-point Representation . . . . . . . . . . . 4<br/>9. 1.2.2Roundingand <br/>10. Chopping. . . . . . . . . . . . . . . . . . . . . 6<br/>11. 1.3 <br/>12. Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br/>13. 1.4Sources <br/>14. Of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br/>15. 1.4.1Human <br/>16. Error. . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br/>17. 1.4.2 <br/>18. Truncation Error . . . . . . . . . . . . . . . . . . . . . . . . . 9<br/>19. 1.4.3Round-o- <br/>20. Error . . . . . . . . . . . . . . . . . . . . . . . . .10<br/>21. 1.5 <br/>22. E-ect of Round-o- Errors in Arithmetic Operation . . . . . . . . . . 10<br/>23. 1.5.1 <br/>24. Rounding o- Errors in Addition and Subtraction . . . . . . . 11<br/>25. 1.5.2 <br/>26. Rounding o- Errors in Multiplication . . . . . . . . . . . . . 12<br/>27. 1.5.3 <br/>28. Roundingo- Errors in Division . . . . . . . . . . . . . . . . . 14<br/>29. 1.5.4 <br/>30. Rounding o- Errors in Powers and roots . . . . . . . . . . . . 16<br/>31. 1.6Summary <br/>32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br/>33. 1.7Exercises <br/>34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br/>35. 2 Solution of Nonlinear Equations 21<br/>36. 2.1 <br/>37. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21<br/>38. 2.2Methodof <br/>39. Bisection . . . . . . . . . . . . . . . . . . . . . . . . . . . 23<br/>40. 2.3 <br/>41. False Position Method . . . . . . . . . . . . . . . . . . . . . . . . . . 29<br/>42. 2.4Fixed-Point <br/>43. Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<br/>44. 2.5Newton's <br/>45. Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44<br/>46. 2.6Secant <br/>47. Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51<br/>48. 2.7Multiplicityofa <br/>49. Root . . . . . . . . . . . . . . . . . . . . . . . . . . 55<br/>50. 2.8 <br/>51. Convergence of Iterative Methods . . . . . . . . . . . . . . . . . . . . 63<br/>52. 2.9 <br/>53. Acceleration of Convergence . . . . . . . . . . . . . . . . . . . . . . . 76<br/>54. 2.10 <br/>55. Systems of Nonlinear Equations . . . . . . . . . . . . . . . . . . . . . 80<br/>56. 2.10.1 <br/>57. Newton's Method. . . . . . . . . . . . . . . . . . . . . . . . . 81<br/>58. Iii<br/>59. Iv Contents <br/>60. 2.11 <br/>61. Rootsofpolynomials. . . . . . . . . . . . . . . . . . . . . . . . . . . 87<br/>62. 2.11.1 <br/>63. Horner'sMethod . . . . . . . . . . . . . . . . . . . . . . . . . 88<br/>64. 2.11.2 <br/>65. Muller'sMethod . . . . . . . . . . . . . . . . . . . . . . . . . 94<br/>66. 2.11.3 <br/>67. Bairstow'sMethod. . . . . . . . . . . . . . . . . . . . . . . . 98<br/>68. 2.12 <br/>69. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103<br/>70. 2.13 <br/>71. Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105<br/>72. 3 Systems of Linear Equations 113<br/>73. 3.1 <br/>74. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113<br/>75. 3.1.1 <br/>76. Linearsysteminmatrixnotation . . . . . . . . . . . . . . .117<br/>77. 3.2 <br/>78. Propertiesofmatricesanddeterminant . . . . . . . . . . . . . . . .119<br/>79. 3.2.1 <br/>80. Introductionofmatrices. . . . . . . . . . . . . . . . . . . . .120<br/>81. 3.2.2 <br/>82. Somespecialmatrixforms . . . . . . . . . . . . . . . . . . .124<br/>83. 3.2.3 <br/>84. Thedeterminantofmatrix . . . . . . . . . . . . . . . . . . .133<br/>85. 3.3 <br/>86. Numericalmethodsforlinearsystems. . . . . . . . . . . . . . . . .140<br/>87. 3.4 <br/>88. Directmethodsforlinearsystems . . . . . . . . . . . . . . . . . . .140<br/>89. 3.4.1 <br/>90. Cramer'sRule . . . . . . . . . . . . . . . . . . . . . . . . . .140<br/>91. 3.4.2 <br/>92. Gaussianeliminationmethod. . . . . . . . . . . . . . . . . . 143<br/>93. 3.4.3 <br/>94. Pivotingstrategies . . . . . . . . . . . . . . . . . . . . . . . .156<br/>95. 3.4.4 <br/>96. Gauss-jordanmethod . . . . . . . . . . . . . . . . . . . . . .162<br/>97. 3.4.5 <br/>98. Ludecompositionmethod . . . . . . . . . . . . . . . . . . . 166<br/>99. 3.4.6 <br/>100. Tridiagonalsystemsoflinearequations . . . . . . . . . . . . 187<br/>101. 3.5 <br/>102. Normsofvectorsandmatrices . . . . . . . . . . . . . . . . . . . . .191<br/>103. 3.5.1 <br/>104. Vectornorms. . . . . . . . . . . . . . . . . . . . . . . . . . .191<br/>105. 3.5.2 <br/>106. Matrixnorms. . . . . . . . . . . . . . . . . . . . . . . . . . .193<br/>107. 3.6 <br/>108. Iterativemethodsforsolvinglinearsystems . . . . . . . . . . . . . 196<br/>109. 3.6.1 <br/>110. Jacobiiterativemethod . . . . . . . . . . . . . . . . . . . . .197<br/>111. 3.6.2 <br/>112. Gauss-seideliterativemethod . . . . . . . . . . . . . . . . . 202<br/>113. 3.6.3 <br/>114. Convergencecriteria. . . . . . . . . . . . . . . . . . . . . . .207<br/>115. 3.7 <br/>116. Eigenvaluesandeigenvectors . . . . . . . . . . . . . . . . . . . . . .212<br/>117. 3.7.1 <br/>118. Successiveover-relaxationmethod . . . . . . . . . . . . . . 220<br/>119. 3.7.2 <br/>120. Conjugategradientmethod. . . . . . . . . . . . . . . . . . . 226<br/>121. 3.8 <br/>122. Conditioningoflinearsystems . . . . . . . . . . . . . . . . . . . . .231<br/>123. 3.8.1 <br/>124. Errorsinsolvinglinearsystems . . . . . . . . . . . . . . . . 231<br/>125. 3.8.2 <br/>126. Iterativere-nement . . . . . . . . . . . . . . . . . . . . . . .242<br/>127. 3.9 <br/>128. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .244<br/>129. 3.10 <br/>130. Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245<br/>131. 4 Approximating Functions 259<br/>132. 4.1 <br/>133. Introduction................................ 259<br/>134. 4.2 <br/>135. Polynomialinterpolationforunevenintervals............. 262<br/>136. 4.2.1 <br/>137. Lagrangeinterpolatingpolynomials .............. 263<br/>138. 4.2.2 <br/>139. Newton'sGeneralInterpolatingFormula............ 274<br/>140. 4.2.3 <br/>141. Aitken'sMethod ......................... 291<br/>142. 4.3 <br/>143. Polynomialinterpolationforevenintervals .............. 294<br/>144. 4.3.1 <br/>145. Forward-di-erences........................ 295<br/>146. 4.3.2 <br/>147. Backward-di-erences....................... 300<br/>148. 4.3.3 <br/>149. Central-di-erences ........................ 303<br/>150. 4.4 <br/>151. Interpolationwithsplinefunctions................... 308<br/>152. 4.4.1 <br/>153. Naturalcubicspline....................... 316<br/>154. 4.4.2 <br/>155. Clampedspline.......................... 317<br/>156. 4.5 <br/>157. Leastsquaresapproximation...................... 320<br/>158. 4.5.1 <br/>159. Linearleastsquares....................... 321<br/>160. 4.5.2 <br/>161. Polynomialleastsquares.................... 326<br/>162. 4.5.3 <br/>163. Nonlinearleastsquares..................... 330<br/>164. 4.5.4 <br/>165. Leastsquaresplane ....................... 338<br/>166. 4.5.5 <br/>167. Overdeterminedlinearsystems ................ 340<br/>168. 4.5.6 <br/>169. Leastsquareswithqrdecomposition............. 343<br/>170. 4.5.7 <br/>171. Leastsquareswithsingularvaluedecomposition ...... 348<br/>172. 4.6 <br/>173. Summary ................................. 353<br/>174. 4.7 <br/>175. Exercises ................................. 354<br/>176. 5 Di-erentiation and Integration 367<br/>177. 5.1 <br/>178. Introduction................................ 367<br/>179. 5.2 <br/>180. Numericaldi-erentiation ........................ 367<br/>181. 5.3 <br/>182. Numericaldi-erentiationformulas................... 369<br/>183. 5.3.1 <br/>184. Firstderivativesformulas.................... 369<br/>185. 5.3.2 <br/>186. Secondderivativesformulas .................. 386<br/>187. 5.4 <br/>188. Formulasforcomputingderivatives .................. 393<br/>189. 5.4.1 <br/>190. Centraldi-erenceformulas................... 393<br/>191. 5.4.2 <br/>192. Forwardandbackwarddi-erenceformulas.......... 394<br/>193. 5.5 <br/>194. Numericalintegration .......................... 395<br/>195. 5.6 <br/>196. Newton-cotesformulas ......................... 397<br/>197. 5.6.1 <br/>198. Closednewton-cotesformulas................. 397<br/>199. 5.6.2 <br/>200. Opennewton-cotesformulas.................. 424<br/>201. 5.7 <br/>202. Repeateduseofthetrapezoidalrule ................. 428<br/>203. 5.8 <br/>204. Rombergintegration........................... 430<br/>205. 5.9 <br/>206. Gaussianquadratures .......................... 433<br/>207. 5.10Summary <br/>208. ................................. 438<br/>209. 5.11Exercises <br/>210. ................................. 439<br/>211. 6 Ordinary Di-erential Equations 447<br/>212. 6.1 <br/>213. Introduction................................ 447<br/>214. 6.1.1 <br/>215. Classi-cationofdi-erentialequations............. 449<br/>216. 6.2 <br/>217. Numericalmethodsforsolvingivp .................. 451<br/>218. 6.3 <br/>219. Single-stepmethodsforivp ...................... 452<br/>220. 6.3.1 <br/>221. Euler'sMethod.......................... 452<br/>222. 6.3.2 <br/>223. Analysisoftheeuler'smethod................. 455<br/>224. 6.3.3 <br/>225. Higher-ordertaylormethods.................. 457<br/>226. 6.3.4 <br/>227. Runge-kuttamethods...................... 460<br/>228. 6.3.5 <br/>229. Third-orderrunge-kuttamethod............... 468<br/>230. 6.3.6 <br/>231. Fourth-orderrunge-kuttamethod .............. 469<br/>232. 6.3.7 <br/>233. Fifth-orderrunge-kuttamethod ............... 472<br/>234. 6.3.8 <br/>235. Runge-Kutta-mersonmethod.................. 473<br/>236. 6.3.9 <br/>237. Runge-Kutta-Lawson'sFifth-ordermethod.......... 475<br/>238. 6.3.10Runge-Kutta-butchersixth-ordermethod <br/>239. .......... 475<br/>240. 6.3.11Runge-Kutta-fehlbergmethod <br/>241. ................. 476<br/>242. 6.4 <br/>243. Multi-stepsmethodsforivp ...................... 478<br/>244. 6.5 <br/>245. Predictor-correctormethods ...................... 485<br/>246. 6.5.1 <br/>247. Milne-simpsonmethod ..................... 486<br/>248. 6.5.2 <br/>249. Adams-Bashforth-moultonmethod............... 489<br/>250. 6.6 <br/>251. Systemsofsimultaneousode ..................... 494<br/>252. 6.7 <br/>253. Higher-orderdi-erentialequations .................. 498<br/>254. 6.8 <br/>255. Boundary-valueproblems........................ 500<br/>256. 6.8.1 <br/>257. Theshootingmethod ...................... 501<br/>258. 6.8.2 <br/>259. Thenonlinearshootingmethod ................ 505<br/>260. 6.8.3 <br/>261. Thefinitedi-erencemethod.................. 507<br/>262. 6.9 <br/>263. Summary ................................. 511<br/>264. 6.10Exercises <br/>265. ................................. 512<br/>266. 7 Eigenvalues and Eigenvectors 517<br/>267. 7.1 <br/>268. Introduction................................ 517<br/>269. 7.2 <br/>270. Linearalgebraandeigenvaluesproblems ............... 527<br/>271. 7.3 <br/>272. Diagonalizationofmatrices ....................... 530<br/>273. 7.4 <br/>274. Basicpropertiesofeigenvalueproblems................ 543<br/>275. 7.5 <br/>276. Someimportantresultsofeigenvalueproblems ........... 560<br/>277. 7.6 <br/>278. Numericalmethodsforeigenvalueproblems ............. 563<br/>279. 7.7 <br/>280. Vectoriterativemethodsforeigenvalues................ 564<br/>281. Contents v <br/>282. Vi Contents <br/>283. 7.7.1 <br/>284. Powermethod .......................... 564<br/>285. Contents vii<br/>286. 7.7.2 <br/>287. Inversepowermethod...................... 569<br/>288. 7.7.3 <br/>289. Shiftedinversepowermethod.................. 572<br/>290. 7.8 <br/>291. Locationofeigenvalues ......................... 576<br/>292. 7.8.1 <br/>293. Gerschgorincirclestheorem .................. 576<br/>294. 7.8.2 <br/>295. Rayleighquotient ........................ 578<br/>296. 7.9 <br/>297. Intermediateeigenvalues......................... 580<br/>298. 7.10eigenvaluesofsymmetricmatrices................... 583<br/>299. 7.10.1jacobimethod <br/>300. .......................... 584<br/>301. 7.10.2sturmsequenceiteration <br/>302. .................... 590<br/>303. 7.10.3Given'sMethod.......................... 594<br/>304. 7.10.4Householder'sMethod...................... 598<br/>305. 7.11matrixdecompositionmethods..................... 602<br/>306. 7.11.1qrmethod............................ 602<br/>307. 7.11.2lrmethod............................ 606<br/>308. 7.11.3upperhessenbergform..................... 609<br/>309. 7.11.4singularvaluedecomposition.................. 616<br/>310. 7.12Summary <br/>311. ................................. 623<br/>312. 7.13Exercises <br/>313. ................................. 624<br/>314. Appendices 634<br/>315. A Some Mathematical Preliminaries 635<br/>316. B Introduction of MATLAB 659<br/>317. C Answers to Selected Exercises 697<br/>318. Bibliography 726<br/>319. Index 727<br/> |
| Withdrawn status | Damaged status | Not for loan | Home library | Current library | Date acquired | Source of acquisition | Full call number | Barcode | Date last seen | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| UE-Central Library | UE-Central Library | 07.06.2018 | U.E. | 518 B9881 | T1776 | 11.03.2020 | 07.06.2018 | Books |
