Endre Süli, David F. Mayers, «An Introduction to Numerical Analysis»
Publisher: Cambridge University Press | Number Of Pages: 444 | Publication Date:2003-09-08 | ISBN / ASIN: 0521007941 | PDF | 4,5 MB
This book has emphasis on analysis of numerical methods, including error bound, consistency, convergence, stability. In most cases, a numerical method is introduced, followed by analysis and proofs. For
engineering students, who like to know more algorithms and a little bit of analysis, this book may not be the best choice. Although this book is mainly about analysis, it does include clear presentation of many numerical methods, including topics in nonlinear equations solving, numerical linear algebra, polynomial interpolation and integration, numerical solution of ODE. In numerical linear algebra, it includes LU factorization with pivoting, Gerschgorin's theorem of eigenvalue positions, Calculating eigenvalues by Jacobi plane rotation, Householder tridiagonalization, Sturm sequence property for tridiagonal symmetric matrix. Interpolation includes Lagrange polynomial, Hermite polynomial, Newton-Cotes integration, Improved Trapezium integration through Romberg method, Oscillation theorem for minimax approximation, Chebyshev polynomial, least square polynomial approximation to a known function, Gauss quadrature using Hermite polynomial, Piecewise linear/cubic splines. Ordinary ddifferential equations section includes initial value problems with one-step and multiple steps, boundary value problems using finite difference and shooting method, Galerkin finite element method. The book gives basic definitions including norms, matrix condition numbers, real symmetric positive definite matrix, Rayleigh quotient, orthogonal polynomials, stiffness, Sobolev space. One place that is not clear is about QR algorithm for tridiagonal matrix.

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2- كتاب " Numerical Analysis"

Rainer Kress " Numerical Analysis"
Springer | 1998-04-17 | ISBN:0387984089 | 344 pages | Djvu | 5,8 Mb

This volume is intended as an introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover all parts of numerical analysis, the goal is to guide the reader towards the basic ideas and general principles by way of considering main and important numerical methods. Given the rapid development of numerical algorithms, a reasonable introduction to numerical analysis has to confine itself to presenting a solid foundation by restricting the presentation to the basic principles and procedures. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis. These are indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. Particular emphasis will be given to the question of stability--especially to well-posedness and ill-posedness. The text is presented in a concise and easily understandable fashion and can be successfully mastered in a one-year course.

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F. Cucker (Editor), P. G. Ciarlet (Editor), Philippe G. Ciarlet (Editor), Jacques Louis Lions (Editor), "Handbook of Numerical Analysis : Special Volume: Foundations of Computational Mathematics"
Pages: 536 | Publisher: Elsevier Science & Technology; Special edition (May 1, 2003) | ISBN: 0444512470 | English | PDF | 4.3 MB

4-كتاب "Theory and Applications of Numerical Analysis, Second Edition

Theory and Applications of Numerical Analysis, Second Edition
Academic Press (1996-01-15) | ISBN: 0125535600 | 447 pages |
PDF | 13.57Mb

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