000 06788nam a2200721Ii 4500
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
041 1 _aeng
050 4 _aQA297
072 7 _aMAT
_x000000
_2bisacsh
072 7 _aMAT
_x003000
_2bisacsh
072 7 _aMAT
_x021000
_2bisacsh
072 7 _aUB
_2bicscc
082 0 4 _a518
100 1 _aRay, Santanu Saha,
_eauthor.
_917868
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].
264 4 _c©2016.
300 _a1 online resource (705 pages) :
_b99 illustrations, text file, PDF
336 _atext
_2rdacontent
337 _acomputer
_2rdamedia
338 _aonline resource
_2rdacarrier
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
650 0 _aEngineering mathematics.
_93254
650 0 _aNumerical analysis.
_94603
650 0 _aNumerical analysis
_xData processing.
_93648
650 7 _aMATHEMATICS / Applied.
_2bisacsh
_96859
650 7 _aMATHEMATICS / Number Systems.
_2bisacsh
_917869
650 7 _aAlgorithms of computation.
_2bisacsh
_917870
650 7 _aAlternating Direction Implicit Method.
_2bisacsh
_917871
650 7 _aApproximation.
_2bisacsh
_917872
650 7 _aboundary value problems.
_2bisacsh
_98596
650 7 _aCubic B-spline.
_2bisacsh
_917873
650 7 _aeigenvalue problems.
_2bisacsh
_917874
650 7 _aFinite Element Method.
_2bisacsh
_917875
650 7 _aGalerkin method.
_2bisacsh
_917876
650 7 _aInterpolation.
_2bisacsh
_92290
650 7 _alinear equations.
_2bisacsh
_917877
650 7 _aNumerical computation.
_2bisacsh
_91832
650 7 _aNumerical differentiation.
_2bisacsh
_917878
650 7 _aNumerical integration.
_2bisacsh
_917879
650 7 _aNumerical Solutions.
_2bisacsh
_917880
650 7 _anumerical algorithms.
_2bisacsh
_917881
650 7 _aOrdinary Differential Equations.
_2bisacsh
_917882
650 7 _apartial Differential Equations.
_2bisacsh
_914385
650 7 _aRoot finding.
_2bisacsh
_917883
655 0 _aElectronic books.
_93294
710 2 _aTaylor and Francis.
_910719
776 0 8 _iPrint version:
_z9781498741743
856 4 0 _uhttps://www.taylorfrancis.com/books/9781315369174
_zClick here to view.
942 _cEBK
999 _c71663
_d71663