Numerical matheatical l analysis/ (Record no. 179920)
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|---|---|
| fixed length control field | 00312nam a2200121Ia 4500 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 518 |
| Item number | SCA/N |
| 245 #0 - TITLE STATEMENT | |
| Title | Numerical matheatical l analysis/ |
| Statement of responsibility, etc. | Scarborough,James B. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New Delhi: |
| Name of publisher, distributor, etc. | Oxford & IBH, |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 600 |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | <br/><br/>2. Approximate Numbers and Significant Figures 2<br/>3. Bounding of Numbers 2<br/>4. Absolute, Relative, and Percentage Errors t<br/>6. Relation between Relative Error and the Number of Significant<br/>Figures 4<br/>6. The General Formula for Errors 8<br/>7. Application of the Error Formulas to the Fundamental Opera<br/>tions of Arithmetic and to Logarithms 10<br/>8. The Impossibility, in General, of Obtaining a Result More<br/>Accurate than the Data Used 20<br/>9. Further Considerations on the Accuracy of a Computed Result 23<br/>10. Accuracy in the Evaluation of a Formula or Complex Ex<br/>pression 24<br/>11. Accuracy in the Determination of Arguments from a Tabulated<br/>Function 28<br/>12. Accuracy of Series Approximations 32<br/>13. Errors in Determinants 39<br/>14. A Final Remark ^<br/>Exercises I<br/>CHAPTER II<br/>INTERPOLATION<br/>differences. NEWTON'S FORMULAS OF INTERPOLATION<br/>15. Introduction<br/>16. Differences • • •<br/>17. Effect of an Error in a Tabular Value 52<br/>18. Relation between Differences and-Derivatives 54<br/>19. Differences of a Polynomial 54<br/>20. Newton's Formula for Forward Interpolation 56<br/>21. Newton's Formula for<br/>Backward Interpolation 59<br/><br/>ziT CONTENTS<br/>CHAPTER III<br/>INTERPOLATION WITH UNEQUAL INTERVALS<br/>OF THE ARGUMENT<br/>ARTICLE PAGE<br/>22. Divided Differences 66<br/>23. Tables of Divided Differences 66<br/>24. Symmetry of Divided Differences 67<br/>25. Relation between Divided Differences and Simple Differences.. 68<br/>26. Newton's General Interpolation Formula 70<br/>27. Lagrange's Interpolation Formula 74<br/>Exercises III<br/>CHAPTER IV<br/>CENTRAL-DIFFERENCE INTERPOLATION FORMULAS<br/>28. Introduction<br/>29. Gauss's Central-Difference Formulas 79<br/>30. Stirling's Interpolation Formula 82<br/>31. Bessel's Interpolation Formulas 84<br/>Exercises IV<br/>32. Definition<br/>CHAPTER V<br/>INVERSE INTERPOLATION<br/>33. By Lagrange's Formula<br/>34. By Successive Approximations •. 93^<br/>36. By Reversion of Series 96<br/>Exercises V<br/>CHAPTER VI<br/>THE ACCURACY OF INTERPOLATION FORMULAS<br/>36. Introduction 102<br/>37. Remainder Term in Newton's Formula (I) and in Lagrange's<br/>Formula<br/>38. Remainder Term in Newton's Formula (II) 104<br/>39. Remainder Term in Stirling's Formula 105<br/>40. Remainder Terms in Bessel's Formulas 106<br/>ARTICLE<br/>CONTENTS XV<br/>41. Recapitulation of Formulas for the Remainder 107<br/>42. Accuracy of Linear Interpolation from Tables 112<br/>Exercises VT<br/>O<br/>CHAPTER VII<br/>INTERPOLATION WITH TWO INDEPENDENT VARIABLES<br/>43. Introduction<br/>TRIGONOMETRIC INTERPOLATION<br/>44. Double Interpolation by a Double Application of Single Inter<br/>polation<br/>45. Double or Two-Way Differences<br/>46. A General Formula for Double Interpolation • 122<br/>47. Trigonometric Interpolation 130<br/>Exercises VII 13<br/>CHAPTER VII<br/>NUMERICAL DIFFERENTIATION AND INTEGRATION<br/>I. NUMERICAL DIFFERENTIATION<br/>48. Numerical Differentiation 133<br/>II. NUMERICAL INTEGRATION<br/>49. Introduction 136<br/>50. A General Quadrature Formula for Equidistant Ordinates.... 136<br/>61. Simpson's Rule 137<br/>52. Weddle's Rule 138<br/>62A. The Trapezoidal Rule /. 142<br/>53. Central-Difference Quadrature Formulas 144<br/>54. Gauss's Quadrature Formula • • 152<br/>55. Lobatto's Formula. 159<br/>56. Tchebycheff's Formula 16?<br/>57. Euler's Formula of Summation and Quadrature 165<br/>58. Caution in the Use of Quadrature Formulas 168<br/>59. Mechanical Cubature 172<br/>60. Prismoids and the Prismoidal Formula 176<br/>Exercises VIII 180<br/>xvi CONTENTS<br/>CHAPTER IX<br/>THE ACCURACY OF QUADRATURE FORMULAS<br/>ARTICLE PAOE<br/>61. IntRoduction 183<br/>62. Formulas for the Inherent Error in Simpson's Rule 183<br/>63. The Inherent Error in Weddle's Rule 189<br/>64. The Remainder Terms in Central-Difference Formulas (53.1)<br/>and (53.3)...; 189<br/>65. The Inherent Errors in the Formulas of Gauss, Lobatto, and<br/>Tchebycheff 191<br/>66. The Remainder Term in Euler's Formula 192<br/>Exercises<br/>IX 193<br/>CHAPTER X<br/>THE SOLUTION OF NUMERICAL ALGEBRAIC AND<br/>TRANSCENDENTAL EQUATIONS<br/>I. EQUATIONS IN ONE UNKNOWN<br/>67. Introduction 194<br/>68. Finding Approximate Values of the Roots 194<br/>68A. Finding Roots by Repeated Application of Location Theorem 195<br/>69. The Method of Interpolation, or of False Position (Regula Falsi) 197<br/>70. Solution by Repeated Plotting on a Larger Scale 199<br/>71. The Newton-Raphson Method 201<br/>72. Geometric Significance of the Newton-Raphson Method 203<br/>73. The Inherent Error in the Newton-Raphson Method 205<br/>74. A Special Procedure for Algebraic Equations 207<br/>75. The Method of Iteration 208<br/>76. Geometry of the Iteration Process 210<br/>77. Convergence of the Iteration Process 211<br/>78. Convergence of the Newton-Raphson Method 212<br/>79. Errors in the Roots due to Errors in the Coefficients and Con<br/>stant Term 213<br/>II. SIMULTANEOUS EQUATIONS IN SEVERAL UNKNOWNS<br/>80. The newton-Raphson Method for Simultaneous Equations 215<br/>81. This Method of Iteration for Simultaneous Equations 219<br/>^^2. Convergence of the Iteration Process in the *Case of Several.<br/>Unknowns 221<br/>Exercises X 223<br/>CONTENTS xvii<br/>CHAPTER XI<br/>GRAEFFE'S ROOT-SQUARING METHOD FOR SOLVING<br/>ABTIOLB<br/>83. Introduction<br/>ALGEBRAIC EQUATIONS<br/>84. Principle of the Method<br/>85. The Root-Squaring Process<br/>86. Case I. Roots Real and Unequal 228<br/>87. A Check on the Coefficients in the Root-Squared Equation 232<br/>88. Case II. Complex Roots<br/>89. Case III. Roots Real and Numerically Equal 243<br/>90. Brodetsky and SmeaPs Improvement of Graeffe's Method 245<br/>91. Improving the Accuracy of the Roots 257<br/>Exercises XI<br/>CHAPTER XII<br/>NUMERICAL SOLUTION OF SIMULTANEOUS LINEAR<br/>EQUATIONS<br/>L SOLUTION BY DETERMINANTS<br/>92. Evaluation of Numerical Determinants 260<br/>93. Cramer's Rule 266<br/>II. SOLUTION BY SUCCESSIVE ELIMINATION OP THE UNKNOWNS<br/>94. The Method of Division by the Leading Coefficients 269<br/>95. The Method of Gauss 272<br/>96. Another Version of the Gauss Method 274<br/>in. SOLUTION BY INVERSION OP MATRICES<br/>97. Definitions 277<br/>98. Addition and Subtraction of Matrices 278<br/>99. Multiplication of Matrices 279<br/>100. Inversion of Matrices ' 284<br/>101. Solution of Equations by Matrix Methods 296<br/>IV. SOLUTION BY ITERATION<br/>102. Systems Solvable by Iteration 297<br/>103. Conditions for the Convergence of the Iteration Process 301<br/>jcviii CONTENTS<br/>ARTICLE<br/>PAGE<br/>104. Errors in the Solutions when the Coefficients and Constant<br/>Terms are Subject to Errors 303<br/>Exercises XII 307<br/>CHAPTER XIII<br/>THE NUMERICAL SOLUTION OF ORDINARY<br/>105. Introduction<br/>DIFFERENTIAL EQUATIONS<br/>I. EQUATIONS OP THE FIRST ORDER<br/>106. Euler's Method and Its Modification 310<br/>107. Picard's Method of Successive Approximations 316<br/>108. Use of Approximating Polynomials 320<br/>109. Methods of Starting the Solution 327<br/>110. Halving the Interval for 334<br/>Exercises XIII<br/>II. EQUATIONS OP THE SECOND ORDER AND SYSTEMS<br/>.OP SIMULTANEOUS EQUATIONS<br/>111. Equations of the Second Order ' 337<br/>112. Second-Order Equations with First Derivative Absent 342<br/>113. Systems of Simultaneous Equations 348<br/>114. Conditions for Convergence 350<br/>III. OTHER METHODS OP SOLVING DIFFERENTIAL<br/>Milne's Method<br/>EQUATIONS NUMERICALLY<br/>The Runge-Kutta Method 35B<br/>Checks, Errors, and Accuracy i - 367<br/>Some General Remarks<br/>Exercises XIV<br/>IV. THE DIFFERENTIAL EQUATIONS OP EXTERIOR BALLISTICS<br/>119. The Simplest Case—Flat EartH with Constant Acceleration of<br/>Gravity <br/>120. The General Case, Allowing for Variation in Air Density with<br/>Altitude<br/>121. Methods of Finding the Starting Values 375<br/>exerciSE XV<br/>ARTICLE<br/>00NTE1JT8<br/>CHAPTER XIV<br/>THE NUMERICAL SOLUTION OF PARTIAL<br/>122. Introduction<br/>DIFFERENTIAL EQUATIONS<br/>I. DIFFERENCE QUOTIENTS AND DIFFERENCE EQUATIONS<br/>123. Difference Quotients 392<br/>124. Difference Equations 394<br/>II. THE METHOD OF ITERATION<br/>125. Solution of Difference Equations by Iteration 396<br/>1216. The Inherent Error in the Solution by Difference Equations.. 406<br/>127. Applications of Conformal Transformation to Certain Problems 407<br/>III. THE METHOD OF RELAXATION<br/>128. Solution of Difference Equations by Relaxation 410<br/>129. Triangular Networks 415<br/>130. Block Relaxation 416<br/>131. The Iteration and Relaxation Methods Compared 420<br/>lY. THE RAYLEIGH-RITZ METHOD<br/>132. Introduction 422<br/>133. The Vibrating String 423<br/>134. Vibration of a Rectangular Membrane 430<br/>135. Comments on the Three Methods 435<br/>CHAPTER XV<br/>NUMERICAL SOLUTION OF INTEGRAL<br/>EQUATIONS<br/>136. Integral Equations—Definitions 437<br/>137. Boundary-Value Problems of Ordinary Differential Equations.<br/>Green's Functions "• > 438<br/>138. Linear Integral Equations 445<br/>139. Non-Linear Integral Equations and Boundary-Value Problems 4<br/>XX CONTENTS<br/>CHAPTER XVI<br/>THE NORMAL LAW OF ERROR AND THE PRINCIPLE<br/>OF LEAST SQUARES<br/>ARTICLE PAOE<br/>140. Errors of Observations and Measurements 460<br/>141. The Law of Accidental Errors 460<br/>142. The Probability of Errors Lying between Given Limits 462<br/>143. The Probability Equation 464<br/>144. The Law of Error of a Linear Function of Independent Quan<br/>tities 468<br/>145. The Probability Integral and Its Evaluation 473<br/>146. The Probability of Hitting a Target 476<br/>147. The Principle of Least Squares 481<br/>148. Weighted Observations 482<br/>149. Residuals 484<br/>150. The Most Probable Value of a Set of Direct Measurements 485<br/>151. Law of Error for Residuals 487<br/>152. Agreement between Theory and Experience 491<br/>Exercises XVI 492<br/>CHAPTER XVII<br/>THE PRECISION OF MEASUREMENTS<br/>153. Measurement, Direct and Indirect • 493<br/>154. Precision and Accuracy 493<br/>I. DIRECT MEASUREMENTS<br/>155. Measures of Precision 494<br/>156. Relations between<br/>the Precision Measures 496<br/>157. Geometric* Significance of /*, r, and 497<br/>158. Relation between Probable Error and Weight, and the Probable<br/>Error of the Arithmetic^ and Weighted Means 499<br/>159. Computation of the Precision Measures from the Residuals.... 500<br/>160. The Combination of Sets of Measurements when the p.e/s of<br/>Sets Are Given 503<br/>Exercises XVII 609<br/>II. INDIRECT MEASUREMENTS<br/>161. The Probable Error of any Function of Independent Quantities<br/>' Whose P.B.'s are Known 510<br/>ABTIO LB<br/>CONTENTS<br/>162. The Two Fundamental Problems of Indirect Measurements... 513<br/>163. Rejection of Observations and Measurements 519<br/>Exercises XVIII 520<br/>164. Introduction<br/>CHAPTER XVII<br/>EMPIRICAL FORMULAS<br/>165. The Graphic Method, or Method of Selected Points 522<br/>166. The Method of Averages. 5^®<br/>166.<br/>167.<br/>The Method of Least Squares 5^^<br/>168. Weighted Residuals 541<br/>169. Non-Linear Formulas—The General Case 545<br/>170. Determination of the Constants when Both Variables Are Sub<br/>ject to Error... 551<br/>171. Finding the Best Type of Formula 554<br/>172. Smoothing of Observational and Experimental Data 556<br/>Exercises XIX 562<br/>CHAPTER XIX<br/>HARMONIC ANALYSIS OF EMPIRICAL FUNCTIONS<br/>178. Introduction <br/>174. Case of 12 Ordinates 564<br/>176. Case of 24 Ordinates<br/>176. Periods other than<br/>Chapter 1: Global Prospects and Policies<br/>Chapter 2: Country and Regional Perspectives<br/>Chapter 3: The Dog That Didn't Bark: Has Inflation Been Muzzled or Was It Just Sleeping?<br/>Chapter 4: Breaking through the Frontier: Can Today's Dynamic Low-Income Countries Make It?<br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Date last checked out | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 518 SCA/N | P34931 | 13/06/2018 | 13/06/2018 | General Books |