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Ordinary Differential Equations

ISBN-10: 0262510189
ISBN-13: 9780262510189
Edition: N/A
List price: $42.00 Buy it from $39.25
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Book details

List price: $42.00
Publisher: MIT Press
Publication date: 7/15/1978
Binding: Paperback
Pages: 290
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.034
Language: English

Preface
Frequently Used Notation
Basic Concepts
Phase Spaces and Phase Flows
Vector Fields on the Line
Phase Flows on the Line
Vector Fields and Phase Flows in the Plane
Nonautonomous Equations
The Tangent Space
Basic Theorems
The Vector Field near a Nonsingular Point
Applications to the Nonautonomous Case
Applications to Equations of Higher Order
Phase Curves of Autonomous Systems
The Directional Derivative. First Integrals
Conservative Systems with One Degree of Freedom
Linear Systems
Linear Problems
The Exponential of an Operator
Properties of the Exponential
The Determinant of the Exponential
The Case of Distinct Real Eigenvalues
Complexification and Decomplexification
Linear Equations with a Complex Phase Space
Complexification of a Real Linear Equation
Classification of Singular Points of Linear Systems
Topological Classification of Singular Points
Stability of Equilibrium Positions
The Case of Purely Imaginary Eigenvalues
The Case of Multiple Eigenvalues
More on Quasi-Polynomials
Nonautonomous Linear Equations
Linear Equations with Periodic Coefficients
Variation of Constants
Proofs of the Basic Theorems
Contraction Mappings
The Existence, Uniqueness, and Continuity Theorems
The Differentiable Manifolds
The Tangent Bundle. Vector Fields on a Manifold
The Phase Flow Determined by a Vector Field
The Index of a Singular Point of a Vector Field
Sample Examination Problems
Bibliography
Index

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