Addolorata Marasco, Antonio Romano

Scientific Computing with Mathematica®

Mathematical Problems for Ordinary Differential Equations

• Broschiertes Buch

Produktbeschreibung

Many interesting behaviors of real physical, biological, economical,and chemical systems can be described by ordinary differentialequations (ODEs).Scientific Computing with Mathematica for Ordinary DifferentialEquationsprovides a general framework useful for the applications, on theconceptual aspects of the theory of ODEs, as well as a sophisticateduse of Mathematica software for the solutions of problems related toODEs. In particular, a chapter is devoted to the use ODEs andMathematica in the Dynamics of rigid bodies.Mathematical methods and scientific computation are dealt with jointlyto supply a unified presentation. The main problems of ordinarydifferential equations suchas, phase portrait, approximate solutions, periodic orbits, stability,bifurcation, andboundary problems are covered in an integrated fashion with numerousworked examples and computer program demonstrations usingMathematica.Topics and Features:_Explains how to use the Mathematica package ODE.mto support qualitative and quantitative problem solving _End-of-chapter exercise sets incorporating the use of Mathematica programs_Detailed description and explanation of the mathematical proceduresunderlying the programs written in Mathematica _Appendix describingthe use of ten notebooks to guide the reader through all theexercises.This book is an essential text/reference for students, graduates andpractitioners in applied mathematics and engineering interested inODE's problems in both the qualitative and quantitative description ofsolutions with the Mathematica program. It is also suitable as a self-

Produktdetails

• Modeling and Simulation in Science, Engineering and Technology
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 978-1-4612-6635-8
• Softcover reprint of the original 1st ed. 2001
• Seitenzahl: 288
• Erscheinungstermin: 19. April 2013
• Englisch
• Abmessung: 235mm x 155mm x 16mm
• Gewicht: 441g
• ISBN-13: 9781461266358
• ISBN-10: 1461266351
• Artikelnr.: 39562995

Inhaltsangabe

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.