000 | 06788nam a2200721Ii 4500 | ||
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001 | 9781315369174 | ||
003 | FlBoTFG | ||
005 | 20220711212603.0 | ||
006 | m o d | ||
007 | cr | ||
008 | 190122t20182016fluab ob 001 0 eng d | ||
020 | _a9781315369174 (e-book : PDF) | ||
035 | _a(OCoLC)960210077 | ||
040 |
_aFlBoTFG _cFlBoTFG _erda |
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041 | 1 | _aeng | |
050 | 4 | _aQA297 | |
072 | 7 |
_aMAT _x000000 _2bisacsh |
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072 | 7 |
_aMAT _x003000 _2bisacsh |
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_aMAT _x021000 _2bisacsh |
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_aUB _2bicscc |
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100 | 1 |
_aRay, Santanu Saha, _eauthor. _917868 |
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245 | 1 | 0 |
_aNumerical Analysis with Algorithms and Programming / _cby Santanu Saha Ray. |
250 | _aFirst edition. | ||
264 | 1 |
_aBoca Raton, FL : _bChapman and Hall/CRC, _c[2018]. |
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264 | 4 | _c©2016. | |
300 |
_a1 online resource (705 pages) : _b99 illustrations, text file, PDF |
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336 |
_atext _2rdacontent |
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337 |
_acomputer _2rdamedia |
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338 |
_aonline resource _2rdacarrier |
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505 | 0 | 0 | _tErrors in Numerical Computations Introduction Preliminary Mathematical Theorems Approximate Numbers and Significant Figures Rounding Off Numbers Truncation Errors Floating Point Representation of Numbers Propagation of Errors General Formula for Errors Loss of Significance Errors Numerical Stability, Condition Number, and Convergence Brief Idea of Convergence ----Numerical Solutions of Algebraic and Transcendental EquationsIntroduction Basic Concepts and Definitions Initial ApproximationIterative Methods Generalized Newtons Method Graeffes Root Squaring Method for Algebraic Equations ----Interpolation Introduction Polynomial Interpolation ----Numerical Differentiation Introduction Errors in Computation of Derivatives Numerical Differentiation for Equispaced Nodes Numerical Differentiation for Unequally Spaced Nodes Richardson Extrapolation ----Numerical Integration Introduction Numerical Integration from Lagranges Interpolation NewtonCotes Formula for Numerical Integration (Closed Type) NewtonCotes Quadrature Formula (Open Type) Numerical Integration Formula from Newtons Forward Interpolation Formula Richardson Extrapolation Romberg Integration Gauss Quadrature Formula Gaussian Quadrature: Determination of Nodes and Weights through Orthogonal Polynomials Lobatto Quadrature Method Double Integration Bernoulli Polynomials and Bernoulli NumbersEulerMaclaurin Formula ----Numerical Solution of System of Linear Algebraic Equations Introduction Vector and Matrix Norm Direct MethodsIterative Method Convergent Iteration Matrices Convergence of Iterative Methods Inversion of a Matrix by the Gaussian Method Ill-Conditioned Systems Thomas Algorithm ----Numerical Solutions of Ordinary Differential Equations Introduction Single-Step Methods Multistep Methods System of Ordinary Differential Equations of First Order Differential Equations of Higher Order Boundary Value Problems Stability of an Initial Value Problem Stiff Differential Equations A-Stability and L-Stability----Matrix Eigenvalue Problem Introduction Inclusion of Eigenvalues Householders Method The QR Method Power Method Inverse Power Method Jacobis Method Givens Method ----Approximation of Functions Introduction Least Square Curve Fitting Least Squares Approximation Orthogonal Polynomials The Minimax Polynomial Approximation B-Splines Pad Approximation ----Numerical Solutions of Partial Differential Equations Introduction Classification of PDEs of Second Order Types of Boundary Conditions and Problems Finite-Difference Approximations to Partial Derivatives Parabolic PDEs Hyperbolic PDEs Elliptic PDEs Alternating Direction Implicit Method Stability Analysis of the Numerical Schemes ----An Introduction to the Finite Element Method Introduction Piecewise Linear Basis Functions The RayleighRitz Method The Galerkin Method ----Bibliography --Answers --Index ----Exercises appear at the end of each chapter. |
520 | 3 | _aNumerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization. Approximation of functions and least square approximation. Numerical differentiation and divided differences, Numerical quadrature and integration, Numerical solutions of ordinary differential equations (ODEs) and boundary value problems, Numerical solution of partial differential equations (PDEs). The text develops students' understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems. | |
530 | _aAlso available in print format. | ||
650 | 0 |
_aAlgorithms. _93390 |
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650 | 0 |
_aEngineering mathematics. _93254 |
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650 | 0 |
_aNumerical analysis. _94603 |
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650 | 0 |
_aNumerical analysis _xData processing. _93648 |
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650 | 7 |
_aMATHEMATICS / Applied. _2bisacsh _96859 |
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650 | 7 |
_aMATHEMATICS / Number Systems. _2bisacsh _917869 |
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650 | 7 |
_aAlgorithms of computation. _2bisacsh _917870 |
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650 | 7 |
_aAlternating Direction Implicit Method. _2bisacsh _917871 |
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650 | 7 |
_aApproximation. _2bisacsh _917872 |
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650 | 7 |
_aboundary value problems. _2bisacsh _98596 |
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650 | 7 |
_aCubic B-spline. _2bisacsh _917873 |
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650 | 7 |
_aeigenvalue problems. _2bisacsh _917874 |
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650 | 7 |
_aFinite Element Method. _2bisacsh _917875 |
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650 | 7 |
_aGalerkin method. _2bisacsh _917876 |
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650 | 7 |
_aInterpolation. _2bisacsh _92290 |
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650 | 7 |
_alinear equations. _2bisacsh _917877 |
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650 | 7 |
_aNumerical computation. _2bisacsh _91832 |
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650 | 7 |
_aNumerical differentiation. _2bisacsh _917878 |
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650 | 7 |
_aNumerical integration. _2bisacsh _917879 |
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650 | 7 |
_aNumerical Solutions. _2bisacsh _917880 |
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650 | 7 |
_anumerical algorithms. _2bisacsh _917881 |
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650 | 7 |
_aOrdinary Differential Equations. _2bisacsh _917882 |
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650 | 7 |
_apartial Differential Equations. _2bisacsh _914385 |
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650 | 7 |
_aRoot finding. _2bisacsh _917883 |
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655 | 0 |
_aElectronic books. _93294 |
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710 | 2 |
_aTaylor and Francis. _910719 |
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776 | 0 | 8 |
_iPrint version: _z9781498741743 |
856 | 4 | 0 |
_uhttps://www.taylorfrancis.com/books/9781315369174 _zClick here to view. |
942 | _cEBK | ||
999 |
_c71663 _d71663 |