Numerical Analysis [electronic resource] /

No applied mathematician can be properly trained without some basic un­ derstanding ofnumerical methods, Le., numerical analysis. And no scientist and engineer should be using a package program for numerical computa­ tions without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool for solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. The book evolved from the courses on numerical analysis I have taught since 1971 at the University ofGottingen and may be viewed as a successor of an earlier version jointly written with Bruno Brosowski [10] in 1974. It aims at presenting the basic ideas of numerical analysis in a style as concise as possible. Its volume is scaled to a one-year course, i.e., a two-semester course, addressing second-yearstudents at a German university or advanced undergraduate or first-year graduate students at an American university.

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Main Authors: Kress, Rainer. author., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: New York, NY : Springer New York : Imprint: Springer, 1998
Subjects:Mathematics., Numerical analysis., Applied mathematics., Engineering mathematics., Numerical Analysis., Appl.Mathematics/Computational Methods of Engineering.,
Online Access:http://dx.doi.org/10.1007/978-1-4612-0599-9
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record_format koha
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Numerical analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Numerical Analysis.
Appl.Mathematics/Computational Methods of Engineering.
Mathematics.
Numerical analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Numerical Analysis.
Appl.Mathematics/Computational Methods of Engineering.
spellingShingle Mathematics.
Numerical analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Numerical Analysis.
Appl.Mathematics/Computational Methods of Engineering.
Mathematics.
Numerical analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Numerical Analysis.
Appl.Mathematics/Computational Methods of Engineering.
Kress, Rainer. author.
SpringerLink (Online service)
Numerical Analysis [electronic resource] /
description No applied mathematician can be properly trained without some basic un­ derstanding ofnumerical methods, Le., numerical analysis. And no scientist and engineer should be using a package program for numerical computa­ tions without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool for solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. The book evolved from the courses on numerical analysis I have taught since 1971 at the University ofGottingen and may be viewed as a successor of an earlier version jointly written with Bruno Brosowski [10] in 1974. It aims at presenting the basic ideas of numerical analysis in a style as concise as possible. Its volume is scaled to a one-year course, i.e., a two-semester course, addressing second-yearstudents at a German university or advanced undergraduate or first-year graduate students at an American university.
format Texto
topic_facet Mathematics.
Numerical analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Numerical Analysis.
Appl.Mathematics/Computational Methods of Engineering.
author Kress, Rainer. author.
SpringerLink (Online service)
author_facet Kress, Rainer. author.
SpringerLink (Online service)
author_sort Kress, Rainer. author.
title Numerical Analysis [electronic resource] /
title_short Numerical Analysis [electronic resource] /
title_full Numerical Analysis [electronic resource] /
title_fullStr Numerical Analysis [electronic resource] /
title_full_unstemmed Numerical Analysis [electronic resource] /
title_sort numerical analysis [electronic resource] /
publisher New York, NY : Springer New York : Imprint: Springer,
publishDate 1998
url http://dx.doi.org/10.1007/978-1-4612-0599-9
work_keys_str_mv AT kressrainerauthor numericalanalysiselectronicresource
AT springerlinkonlineservice numericalanalysiselectronicresource
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spelling KOHA-OAI-TEST:1903732018-07-30T23:14:18ZNumerical Analysis [electronic resource] / Kress, Rainer. author. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1998.engNo applied mathematician can be properly trained without some basic un­ derstanding ofnumerical methods, Le., numerical analysis. And no scientist and engineer should be using a package program for numerical computa­ tions without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool for solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. The book evolved from the courses on numerical analysis I have taught since 1971 at the University ofGottingen and may be viewed as a successor of an earlier version jointly written with Bruno Brosowski [10] in 1974. It aims at presenting the basic ideas of numerical analysis in a style as concise as possible. Its volume is scaled to a one-year course, i.e., a two-semester course, addressing second-yearstudents at a German university or advanced undergraduate or first-year graduate students at an American university.1 Introduction -- 2 Linear Systems -- 2.1 Examples for Systems of Equations -- 2.2 Gaussian Elimination -- 2.3 LR Decomposition -- 2.4 QR Decomposition -- Problems -- 3 Basic Functional Analysis -- 3.1 Normed Spaces -- 3.2 Scalar Products -- 3.3 Bounded Linear Operators -- 3.4 Matrix Norms -- 3.5 Completeness -- 3.6 The Banach Fixed Point Theorem -- 3.7 Best Approximation -- Problems -- 4 Iterative Methods for Linear Systems -- 4.1 Jacobi and Gauss—Seidel Iterations -- 4.2 Relaxation Methods -- 4.3 Two-Grid Methods -- Problems -- 5 Ill-Conditioned Linear Systems -- 5.1 Condition Number -- 5.2 Singular Value Decomposition -- 5.3 Tikhonov Regularization -- Problems -- 6 Iterative Methods for Nonlinear Systems -- 6.1 Successive Approximations -- 6.2 Newton’s Method -- 6.3 Zeros of Polynomials -- 6.4 Least Squares Problems -- Problems -- 7 Matrix Eigenvalue Problems -- 7.1 Examples -- 7.2 Estimates for the Eigenvalues -- 7.3 The Jacobi Method -- 7.4 The QR Algorithm -- 7.5 Hessenberg Matrices -- Problems -- 8 Interpolation -- 8.1 Polynomial Interpolation -- 8.2 Trigonometric Interpolation -- 8.3 Spline Interpolation -- 8.4 Bézier Polynomials -- Problems -- 9 Numerical Integration -- 9.1 Interpolatory Quadratures -- 9.2 Convergence of Quadrature Formulae -- 9.3 Gaussian Quadrature Formulae -- 9.4 Quadrature of Periodic Functions -- 9.5 Romberg Integration -- 9.6 Improper Integrals -- Problems -- 10 Initial Value Problems -- 10.1 The Picard—Lindelöf Theorem -- 10.2 Euler’s Method -- 10.3 Single-Step Methods -- 10.4 Multistep Methods -- Problems -- 11 Boundary Value Problems -- 11.1 Shooting Methods -- 11.2 Finite Difference Methods -- 11.3 The Riesz and Lax-Milgram Theorems -- 11.4 Weak Solutions -- 11.5 The Finite Element Method -- Problems -- 12 Integral Equations -- 12.1 The Riesz Theory -- 12.2 Operator Approximations -- 12.3 Nyström’s Method -- 12.4 The Collocation Method -- 12.5 Stability -- Problems -- References.No applied mathematician can be properly trained without some basic un­ derstanding ofnumerical methods, Le., numerical analysis. And no scientist and engineer should be using a package program for numerical computa­ tions without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool for solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. The book evolved from the courses on numerical analysis I have taught since 1971 at the University ofGottingen and may be viewed as a successor of an earlier version jointly written with Bruno Brosowski [10] in 1974. It aims at presenting the basic ideas of numerical analysis in a style as concise as possible. Its volume is scaled to a one-year course, i.e., a two-semester course, addressing second-yearstudents at a German university or advanced undergraduate or first-year graduate students at an American university.Mathematics.Numerical analysis.Applied mathematics.Engineering mathematics.Mathematics.Numerical Analysis.Appl.Mathematics/Computational Methods of Engineering.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-0599-9URN:ISBN:9781461205999