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Scientific Computing with Mathematica

Mathematical Problems for Ordinary Differential Equations - Book with CD-ROM
BuchGebunden
270 Seiten
Englisch
Springererschienen am09.08.2001Repr. d. Ausg. v. 2001
Many behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). This book provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, and a sophisticated use of Mathematica software for the solutions of problems related to ODEs.mehr
Verfügbare Formate
BuchGebunden
EUR106,99
BuchKartoniert, Paperback
EUR106,99
E-BookPDF1 - PDF WatermarkE-Book
EUR96,29

Produkt

KlappentextMany behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). This book provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, and a sophisticated use of Mathematica software for the solutions of problems related to ODEs.
Zusammenfassung
Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-0-8176-4205-1
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2001
Erscheinungsdatum09.08.2001
AuflageRepr. d. Ausg. v. 2001
ReiheModeling and Simulation in Science, Engineering and Technology
Seiten270 Seiten
SpracheEnglisch
Gewicht585 g
IllustrationenXIV, 270 p.
Artikel-Nr.11766251

Inhalt/Kritik

Inhaltsverzeichnis
1 Solutions of ODEs and Their Properties.- 1.1 Introduction.- 1.2 Definitions and Existence Theory.- 1.3 Functions DSolve, NDSolve, and Differentiallnvariants.- 1.4 The Phase Portrait.- 1.5 Applications of the Programs Sysn, Phase2D, PolarPhase, and Phase3D.- 1.6 Problems.- 2 Linear ODEs with Constant Coefficients.- 2.1 Introduction.- 2.2 The General Solution of Linear Differential Systems with Constant Coefficients.- 2.3 The Program LinSys.- 2.4 Problems.- 3 Power Series Solutions of ODEs and Frobenius Series.- 3.1 Introduction.- 3.2 Power Series and the Program Taylor.- 3.3 Power Series and Solutions of ODEs.- 3.4 Series Solutions Near Regular Singular Points: Method of Frobenius.- 3.5 The Program SerSol.- 3.6 Other Applications of SerSol.- 3.7 The Program Frobenius.- 3.8 Problems.- 4 Poincaré´s Perturbation Method.- 4.1 Introduction.- 4.2 Poincaré´s Perturbation Method.- 4.3 How to Introduce the Small Parameter.- 4.4 The Program Poincare.- 4.5 Problems.- 5 Problems of Stability.- 5.1 Introduction.- 5.2 Definitions of Stability.- 5.3 Analysis of Stability: The Direct Method.- 5.4 Polynomial Liapunov Functions.- 5.5 The Program Liapunov.- 5.6 Analysis of Stability, the Indirect Method: The Planar Case.- 5.7 The Program LStability.- 5.8 Problems.- 6 Stability: The Critical Case.- 6.1 Introduction.- 6.2 The Planar Case and Poincaré´s Method.- 6.3 The Programs CriticalEqS and CriticalEqN.- 6.4 The Center Manifold.- 6.5 The Program CManifold.- 6.6 Problems.- 7 Bifurcation in ODEs.- 7.1 Introduction to Bifurcation.- 7.2 Bifurcation in a Differential Equation Containing One Parameter.- 7.3 The Programs Bifl and Bif1G.- 7.4 Problems.- 7.5 Bifurcation in a Differential Equation Depending on Two Parameters.- 7.6 The Programs Bif2 and Bif2G.- 7.7 Problems.- 7.8 Hopf´sBifurcation.- 7.9 The Program HopfBif.- 7.10 Problems.- 8 The Lindstedt-Poincaré Method.- 8.1 Asymptotic Expansions.- 8.2 The Lindstedt-Poincaré Method.- 8.3 The Programs LindPoinc and GLindPoinc.- 8.4 Problems.- 9 Boundary-Value Problems for Second-Order ODEs.- 9.1 Boundary-Value Problems and Bernstein´s Theorem.- 9.2 The Shooting Method.- 9.3 The Program NBoundary.- 9.4 The Finite Difference Method.- 9.5 The Programs NBoundaryl and NBoundary2.- 9.6 Problems.- 10 Rigid Body with a Fixed Point.- 10.1 Introduction.- 10.2 Euler´s Equations.- 10.3 Free Rotations or Poinsot´s Motions.- 10.4 Heavy Gyroscope.- 10.5 The Gyroscopic Effect.- 10.6 The Program Poinsot.- 10.7 The Program Solid.- 10.8 Problems.- A How to Use the Package ODE.m.- References.mehr

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