| Preface |
| Solutions of ODEs and Their Properties / 1： |
| Introduction / 1.1： |
| Definitions and Existence Theory / 1.2： |
| Functions DSolve, NDSolve, and DifferentialInvariants / 1.3： |
| The Phase Portrait / 1.4： |
| Applications of the Programs Sysn, Phase2D, PolarPhase, and Phase3D / 1.5： |
| Problems / 1.6： |
| Linear ODEs with Constant Coefficients / 2： |
| The General Solution of Linear Differential Systems with Constant Coefficients / 2.1： |
| The Program LinSys / 2.3： |
| Power Series Solutions of ODEs and Frobenius Series / 2.4： |
| Power Series and the Program Taylor / 3.1： |
| Power Series and Solutions of ODEs / 3.3： |
| Series Solutions Near Regular Singular Points: Method of Frobenius / 3.4： |
| The Program SerSol / 3.5： |
| Other Applications of SerSol / 3.6： |
| The Program Frobenius / 3.7： |
| Poincare's Perturbation Method / 3.8： |
| How to Introduce the Small Parameter / 4.1： |
| The Program Poincare / 4.4： |
| Problems of Stability / 4.5： |
| Definitions of Stability / 5.1： |
| Analysis of Stability: The Direct Method / 5.3： |
| Polynomial Liapunov Functions / 5.4： |
| The Program Liapunov / 5.5： |
| Analysis of Stability, the Indirect Method: The Planar Case / 5.6： |
| The Program LStability / 5.7： |
| Stability: The Critical Case / 5.8： |
| The Planar Case and Poincare's Method / 6.1： |
| The Programs CriticalEqS and CriticalEqN / 6.3： |
| The Center Manifold / 6.4： |
| The Program CManifold / 6.5： |
| Bifurcation in ODEs / 6.6： |
| Introduction to Bifurcation / 7.1： |
| Bifurcation in a Differential Equation Containing One Parameter / 7.2： |
| The Programs Bif1 and Bif1G / 7.3： |
| Bifurcation in a Differential Equation Depending on Two Parameters / 7.4： |
| The Programs Bif2 and Bif2G / 7.6： |
| Hopf's Bifurcation / 7.7： |
| The Program HopfBif / 7.9： |
| The Lindstedt-Poincare Method / 7.10： |
| Asymptotic Expansions / 8.1： |
| The Programs LindPoinc and GLindPoinc / 8.2： |
| Boundary-Value Problems for Second-Order ODEs / 8.4： |
| Boundary-Value Problems and Bernstein's Theorem / 9.1： |
| The Shooting Method / 9.2： |
| The Program NBoundary / 9.3： |
| The Finite Difference Method / 9.4： |
| The Programs NBoundary1 and NBoundary2 / 9.5： |
| Rigid Body with a Fixed Point / 9.6： |
| Euler's Equations / 10.1： |
| Free Rotations or Poinsot's Motions / 10.3： |
| Heavy Gyroscope / 10.4： |
| The Gyroscopic Effect / 10.5： |
| The Program Poinsot / 10.6： |
| The Program Solid / 10.7： |
| How to Use the Package ODE.m / 10.8： |
| The Notebooks for Using ODE.m / A.1： |
| A Brief Introduction to Programming / A.2： |
| The Structure of Program Sysn / A.3： |
| References |
| Index |
| Preface |
| Solutions of ODEs and Their Properties / 1： |
| Introduction / 1.1： |
図書
