Numerical analysis for applied science / / Myron B. Allen III, Eli L. Isaacson

• Autore: Allen Myron B. <1954->
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 1998; ©1998
• Descrizione fisica: 1 online resource (512 p.)
• Disciplina: 515
• Soggetto topico: Numerical analysis
• Persona (resp. second.): IsaacsonEli L.
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Numerical Analysis for Applied Science; CONTENTS; Preface; 0 Some Useful Tools; 0.1 Introduction; 0.2 Bounded Sets; 0.3 Normed Vector Spaces; 0.4 Results from Calculus; 0.5 Problems; 0.6 References; 1 Approximation of Functions; 1.1 Introduction; 1.2 Polynomial Interpolation; 1.3 Piecewise Polynomial Interpolation; 1.4 Hermite Interpolation; 1.5 Interpolation in Two Dimensions; 1.6 Splines; 1.7 Least-Squares Methods; 1.8 Trigonometric Interpolation; 1.9 Problems; 1.10 References; 2 Direct Methods for Linear Systems; 2.1 Introduction; 2.2 Gauss Elimination; 2.3 Variants of Gauss Elimination ; 2.4 Band Matrices2.5 Matrix Norms; 2.6 Errors and Iterative Improvement; 2.7 Problems; 2.8 References; 3 Solution of Nonlinear Equations; 3.1 Introduction; 3.2 Bisection; 3.3 Successive Substitution in One Variable; 3.4 Newton's Method in One Variable; 3.5 The Secant Method; 3.6 Successive Substitution: Several Variables; 3.7 Newton's Method: Several Variables; 3.8 Problems; 3.9 References; 4 Iterative Methods for Linear Systems; 4.1 Introduction; 4.2 Conceptual Foundations; 4.3 Matrix-Splitting Techniques; 4.4 Successive Overrelaxation; 4.5 The Conjugate-Gradient Method; 4.6 Problems ; 4.7 References5 Eigenvalue Problems; 5.1 Basic Facts About Eigenvalues; 5.2 Power Methods; 5.3 The QR Method: Underlying Concepts; 5.4 The QR Method Implementation; 5.5 Problems; 5.6 References; 6 Numerical Integration; 6.1 Introduction; 6.2 Newton-Cotes Formulas; 6.3 Romberg and Adaptive Quadrature; 6.4 Gauss Quadrature; 6.5 Problems; 6.6 References; 7 Ordinary Differential Equations; 7.1 Introduction; 7.2 One-Step Methods; 7.3 Multistep Methods: Consistency and Stability; 7.4 Convergence of Multistep Methods; 7.5 Problems; 7.6 References; 8 Difference Methods for PDEs; 8.1 Introduction ; 8.2 The Poisson Equation8.3 The Advection Equation; 8.4 Other Time-Dependent Equations; 8.5 Problems; 8.6 References; 9 Introduction to Finite Elements; 9.1 Introduction and Background; 9.2 A Steady-State Problem; 9.3 A Transient Problem; 9.4 Problems; 9.5 References; Appendix A: Divided Differences; Appendix B: Local Minima; Appendix C: Chebyshev Polynomials; Index
• Sommario/riassunto: Written for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in ""Numerical Analysis"" and ""Numerical Methods."" It will combine the material of both these areas as well as special topics in modern applications. Included at the end of each chapter are a variety of theoretical and computational exercises.
• Titolo autorizzato: Numerical analysis for applied science
• ISBN: 1-118-03312-4; 1-118-03027-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910141239503321
• Lo trovi qui: Univ. Federico II
• Serie: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts