Introductory methods of numerical analysis / (Record no. 1983)
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000 -LEADER | |
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fixed length control field | 07643nam a2200169 a 4500 |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9788120327610 (pbk.) : |
040 ## - CATALOGING SOURCE | |
Transcribing agency | CUS |
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 005.1 |
Item number | SAS/I |
100 1# - MAIN ENTRY--PERSONAL NAME | |
Personal name | Sastry, S. S. |
245 10 - TITLE STATEMENT | |
Title | Introductory methods of numerical analysis / |
Statement of responsibility, etc. | S.S. Sastry. |
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
Place of publication, distribution, etc. | New Delhi : |
Name of publisher, distributor, etc. | Prentice-Hall of India, |
Date of publication, distribution, etc. | 2005. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | 440 p. : |
Other physical details | ill. ; |
Dimensions | 23 cm. |
500 ## - GENERAL NOTE | |
General note | Includes index. |
505 ## - FORMATTED CONTENTS NOTE | |
Formatted contents note | 1. Errors in Numerical Calculations<br/>1.1 Introduction 1<br/>1.1.1 Computer and Nmnerical Software 3<br/>1.1.2 Computer Languages 3<br/>1.1.3 So^are Packages 4<br/>1.2 Mathematical Preliminaries 5<br/>1.3 Errors and Their Con:q)utations 7<br/>1.4 A General Error Formula 11<br/>1.5 Error in a Series Approximation 12<br/>Exercises 17<br/>2. Solution of Algebraic and Transcendental Equations<br/>2.1 Introduction 20<br/>2.2 The Bisection Method 21<br/>2.3 The Method of False Position 24<br/>2.4 The Iteration Method 26<br/>2.5 Newton-Raphson Method 33<br/>2.6 Ramanujan's Method 38<br/>2.7 The Secant Method 43<br/>2.8 Muller's Method 44<br/>2.9 Graeffe's Root-squaring Method 46<br/>2.10 Lin-Bairstow's Method 48<br/>2.11 The Quotient-difference Method 51<br/>2.12 Solution to Systems of Nonlinear Equations 54<br/>2.12.1 The Method of Iteration 54<br/>2.12.2 Newton-Raphson Method 57<br/>Exercises 59<br/>3. Interpolation<br/>3.1 Introduction 63<br/>3.2 Errors in Polynomial Interpolation 64<br/>3.3 Finite Differences 65<br/>3.3.1 Forward Differences 65<br/>3.3.2 Backward Differences 66<br/>3.3.3 Central Differences 67<br/>3.3.4 Symbolic Relations and Separation of<br/>Symbols 68<br/>3.4 Detection of Errors by Use of Difference Tables 71<br/>3.5 Differences of a Polynomial 72<br/>3.6 Newton's Formulae for Interpolation 73<br/>3.7 Central Difference Interpolation Formulae 7P<br/>3.7.1 Gauss' Central Difference Formulae 79<br/>3.7.2 Stirling's Formula 83<br/>3.7.3 Bessel's Formula 83<br/>3.7A Everett's Formula 85<br/>3.7.5 Relation between Bessel's and Everett's<br/>Formulae 85<br/>3.8 Practical Interpolation 86<br/>3.9 Interpolation with Unevenly Spaced Points 90<br/>3.9.1 Lagrange's Interpolation Formula 91<br/>3.9.2 Error in Lagrange's Interpolation Formula 96<br/>3.9.3 Hermite's Interpolation Formula 97<br/>3.10 Divided Differences and Their Properties 100<br/>3.10.1 Newton's General Interpolation Formula 102<br/>3.10.2 Interpolation by Iteration 104<br/>3.11 Inverse Interpolation 105<br/>3.12 Double Interpolation 107<br/>3.13 Spline Interpolation 108<br/>3.13.1 Linear Splines 109<br/>3.13.2 Quadratic Splines 110<br/>3.14 Cubic Splines 112<br/>3.14.1 Minimizing Property of Cubic Splines 117<br/>3.14.2 Error in the Cubic Spline and Its Derivatives 119<br/>3.15 Surface Fitting by Cubic Splines 122<br/>Exercises 125<br/>4. Least Squares, B-splines and Fourier Transforms 137—186<br/>4.1 Introduction 137<br/>4.2 Least-squares Curve Fitting Procedures 138<br/>4.2.1 Fitting a Straight Line 138<br/>4.2.2 Nonlinear Curve Fitting 140<br/>4.2.3 Curve Fitting by a Sum of Exponentials 143<br/>4.3 Weighted Least Squares Approximation 146<br/>4.3.1 Linear Weighted Least Squares Approximation 146<br/>4.3.2 Nonlinear Weighted Least Squares<br/>Approximation 148<br/>4.4 Method of Least Squares for Continuous Functions 149<br/>4.4.1 Orthogonal Polynomials 151<br/>4.4.2 Gram-Schmidt Orthogonalization Process 154<br/>4.5 Cubic B-splines 157<br/>4.5.1 Least-squares Solution 159<br/>4.5.2 Representations of B-splines 159<br/>4.5.3 Computation of B-splines 162<br/>4.6 Fourier Approximation 164<br/>4.6.1 The Fourier Transform 167<br/>4.6.2 The Fast Fourier Transform 169<br/>4.6.3 Cooley-Tukey Algorithm 170<br/>4.6.4 Sande-Tukey Algorithm 176<br/>4.6.5 Computation of the Inverse DFT 177<br/>4.7 Approximation of Fimctions 178<br/>4.7.1 Chebyshev Polynomials 178<br/>4.7.2 Economization of Power Series 181<br/>Exercises 182<br/>5. Numerical Dinerentiatlou and Integration<br/>5.1 Introduction 187<br/>5.2 Numerical Differentiation 187<br/>5.2.1 Errors in Numerical Differentiation 192<br/>5.2.2 The Cubic Spline Method 194<br/>5.3 Maximum and Minimum Values of a Tabulated<br/>Function 196<br/>5.4 Numerical Integration 197<br/>5.4.1 Trapezoidal Rule 198<br/>5.4.2 Simpson's 1/3-Rule 200<br/>5.4.3 Simpson's 3/8-Rule 201<br/>5.4.4 Boole's and Weddle's Rules 201<br/>5.4.5 Use of Cubic Splines 202<br/>5.4.6 Romberg Integration 202<br/>5.4.7 Newton-Cotes Integration Formulae 204<br/>5.5 Euler-Maclaurin Formula 211<br/>5.6 Adaptive Quadratxire Methods 213<br/>5.7 Gaussian Integration 216<br/>5.8 Numerical Evaluation of Singular Integrals 220<br/>5.8.1 Evaluation of Principal Value Integrals 220<br/>5.8.2 Generalized Quadrature 222<br/>5.9 Numerical Calculation of Fourier Integrals 224<br/>5.9.1 Trapezoidal Rule 224<br/>5.9.2 Filon's Formula 225<br/>5.9.3 The Cubic Spline Method 227<br/>5.10 Numerical Double Integration 230<br/>Exercises 232<br/>6. Matrices and Linear Systems of Equations<br/>6.1 Introduction 240<br/>6.2 Basic Definitions 240<br/>6.2.1 Matrix Operations 243<br/>6.2.2 Transpose of a Matrix 245<br/>6.2.3 The hiverse of a Matrix 248<br/>6.2.4 Rank of a Matrix 249<br/>6.2.5 Consistency of a Linear System of<br/>Equations 250<br/>6.2.6 Vector and Matrix Norms 252<br/>6.3 Solution of Linear Systems—^Direct Methods 255<br/>6.3.1 Matrix Inversion Method 255<br/>6.3.2 Gauss Elimination 257<br/>6.3.3 Gauss-Jordan Method 260<br/>6.3.4 Modification of the Gauss Method to Compute<br/>the Inverse 261<br/>6.3.5 Number of Arithmetic Operations 264<br/>6.3.6 LU Decomposition 265<br/>6.3.7 LU Decomposition firom Gauss Elimination 269<br/>6.3.8 Solution of Tridiagonal Systems 270<br/>6.3.9 Solution of Centro-symmetric Equations 271<br/>6.3.10 Ill-conditioned Linear Systems 272<br/>6.3.11 Method for Ill-conditioned Matrices 274<br/>6.4 Solution of Linear Systems—Alterative Methods 275<br/>6.5 The Eigenvalue Problem 278<br/>6.5.1 Eigenvalues of a Symmetric Tridiagonal<br/>Matrix 282<br/>6.5.2 Householder's Method 283<br/>6.5.3 The QR Method 287<br/>6.6 Singular Value Decompoisition 288<br/>Exercises 290<br/>7. Numerical Solution of Ordinary Differential Equations 295-332<br/>7.1 Introduction 295<br/>7.2 Solution by Taylor's Series 296<br/>7.3 Picard's Method of Successive Approximations 298<br/>7.4 Euler's Method 300<br/>7.4.1 Error Estimates for the Euler Method 301<br/>7.4.2 Modified Euler's Method 303<br/>7.5 Runge-Kutta Methods 304<br/>7.6 Predictor-Corrector Methods 309<br/>7.6.1 Adams-Moulton Method 309<br/>7.6.2 Milne's Method 311<br/>7.7 The Cubic Spline Method 314<br/>7.8 Simultaneous and Higher-order Equations 316<br/>7.9 Some General Remarks 317<br/>7.10 Boundary-value Problems 318<br/>7.10.1 Finite-difference Method 318<br/>7.10.2 The Shooting Method 323<br/>7.10.3 The Cubic Spline Method 325<br/>Exercises. 328<br/>8. Numerical Solution of Partial Differential Equations<br/>8.1 Introduction 333<br/>8.2 Finite-Difference Approximations to Derivatives 335<br/>8.3 Laplace's Equation 338<br/>8.3.1 Jacobi's Method 339<br/>8.3.2 Gauss-Seidel Method 339<br/>8.3.3 Successive Over-relaxation (or SOR<br/>Method) 339<br/>8.3.4 The ADI Method 345<br/>8.4 Parabolic Equations 349<br/>8.5 Iterative Methods for the Solution of Equations 355<br/>8.6 Hyperbolic Equations 358<br/>8.7 Software for Partial Differential Equations 362<br/>Exercises 362<br/>9. Numerical Solution of Integral Equations<br/>9.1 Introduction 365<br/>9.2 Numerical Methods for Fredholm Equations 367<br/>9.2.1 Method of Degenerate Kernels 367<br/>9.2.2 Quadrature Methods 370<br/>9.2.3 Use of Chebyshev Series 372<br/>9.2.4 The Cubic Spline Method 376<br/>9.3 Singular Kernels 378<br/>9.4 Method of Invariant Imbedding 382<br/>Exercises 385<br/>10. The Finite Element Method<br/>10.1 Introduction 387<br/>10.1.1 Functionals 388<br/>10.1.2 Base Fimctions 392<br/>10.2 Methods of Approximation 392<br/>10.2.1 The Rayleigh-Ritz Method 393<br/>10.2.2 The Galerkin Method 399<br/>10.3 Application to Two-dimensional Problems 401<br/>10.4 The Finite Element Method 402<br/>10.4.1 Finite Element Method for One-dimensional<br/>Problems 404<br/>10.4.2 Application to Two-dimensional Problems 411<br/>10.5 Concluding Remarks 419<br/>Exercises 419 |
650 #0 - SUBJECT | |
Keyword | Numerical analysis. |
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 |
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Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 02/06/2016 | 005.1 SAS/I | P18996 | 14/07/2018 | 14/07/2018 | General Books | ||||
Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 02/06/2016 | 005.1 SAS/I | P19000 | 14/07/2018 | 14/07/2018 | General Books | ||||
Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 02/06/2016 | 005.1 SAS/I | P18998 | 14/07/2018 | 14/07/2018 | General Books | ||||
Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 02/06/2016 | 005.1 SAS/I | P18999 | 02/06/2016 | General Books | |||||
Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 02/06/2016 | 005.1 SAS/I | P18997 | 14/07/2018 | 14/07/2018 | General Books |