Author | Marasco, Addolorata. author |
---|---|
Title | Scientific Computing with Mathematicaยฎ [electronic resource] : Mathematical Problems for Ordinary Differential Equations / by Addolorata Marasco, Antonio Romano |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0151-9 |
Descript | XIV, 270 p. online resource |
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 Poincarรฉโs Perturbation Method -- 4.1 Introduction -- 4.2 Poincarรฉโs 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 Poincarรฉโs 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 Hopfโs Bifurcation -- 7.9 The Program HopfBif -- 7.10 Problems -- 8 The Lindstedt-Poincarรฉ Method -- 8.1 Asymptotic Expansions -- 8.2 The Lindstedt-Poincarรฉ 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 Bernsteinโs 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 Eulerโs Equations -- 10.3 Free Rotations or Poinsotโs 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