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Numerical Methods for Ordinary Differential Equations
Initial Value Problems
Taschenbuch von David F Griffiths (u. a.)
Sprache: Englisch

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Beschreibung

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge-Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via [...]

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge-Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via [...]

Zusammenfassung

Focuses on the analysis of numerical methods without losing sight of the practical nature of the subject

Covers topics traditionally treated in a first course, but also highlights new and emerging themes

Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples

Includes supplementary material: [...]

Request lecturer material: [...]

Inhaltsverzeichnis
ODEs-An Introduction.- Euler's Method.- The Taylor Series Method.- Linear Multistep Methods-I: Construction and Consistency.- Linear Multistep Methods-II: Convergence and Zero-Stability.- Linear Multistep Methods-III: Absolute Stability.- Linear Multistep Methods-IV: Systems of ODEs.- Linear Multistep Methods-V: Solving Implicit Methods.- Runge-Kutta Method-I: Order Conditions.- Runge-Kutta Methods-II Absolute Stability.- Adaptive Step Size Selection.- Long-Term Dynamics.- Modified Equations.- Geometric Integration Part I-Invariants.- Geometric Integration Part II-Hamiltonian Dynamics.- Stochastic Differential Equations.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
271 S.
69 s/w Illustr.
271 p. 69 illus.
ISBN-13: 9780857291479
ISBN-10: 0857291475
Sprache: Englisch
Herstellernummer: 80023977
Einband: Kartoniert / Broschiert
Autor: Griffiths, David F
Higham, Desmond J
Auflage: 2010 edition
Hersteller: Springer London
Springer-Verlag London Ltd.
Maße: 236 x 156 x 20 mm
Von/Mit: David F Griffiths (u. a.)
Erscheinungsdatum: 25.11.2010
Gewicht: 0,464 kg
Artikel-ID: 107297617
Zusammenfassung

Focuses on the analysis of numerical methods without losing sight of the practical nature of the subject

Covers topics traditionally treated in a first course, but also highlights new and emerging themes

Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples

Includes supplementary material: [...]

Request lecturer material: [...]

Inhaltsverzeichnis
ODEs-An Introduction.- Euler's Method.- The Taylor Series Method.- Linear Multistep Methods-I: Construction and Consistency.- Linear Multistep Methods-II: Convergence and Zero-Stability.- Linear Multistep Methods-III: Absolute Stability.- Linear Multistep Methods-IV: Systems of ODEs.- Linear Multistep Methods-V: Solving Implicit Methods.- Runge-Kutta Method-I: Order Conditions.- Runge-Kutta Methods-II Absolute Stability.- Adaptive Step Size Selection.- Long-Term Dynamics.- Modified Equations.- Geometric Integration Part I-Invariants.- Geometric Integration Part II-Hamiltonian Dynamics.- Stochastic Differential Equations.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
271 S.
69 s/w Illustr.
271 p. 69 illus.
ISBN-13: 9780857291479
ISBN-10: 0857291475
Sprache: Englisch
Herstellernummer: 80023977
Einband: Kartoniert / Broschiert
Autor: Griffiths, David F
Higham, Desmond J
Auflage: 2010 edition
Hersteller: Springer London
Springer-Verlag London Ltd.
Maße: 236 x 156 x 20 mm
Von/Mit: David F Griffiths (u. a.)
Erscheinungsdatum: 25.11.2010
Gewicht: 0,464 kg
Artikel-ID: 107297617
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