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Lectures on Ordinary Differential Equations

Witold Hurewicz
Publisher: 
Dover Publications
Publication Date: 
2002
Number of Pages: 
144
Format: 
Hardcover
Series: 
Dover Phoneix Editions
Price: 
27.50
ISBN: 
0486495108
Category: 
Textbook
BLL Rating: 

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Preface
  Witold Hurewicz In Memoiam
  Chapter 1 Differential Equations of the First Order in One Unknown Function
    PART A THE CAUCHY-EULER APPROXIMATION METHOD
    Section 1 Definitions. Direction Fields
    2 Approximate Solutions of the Differential Equation
    3 The Fundamental Inequality
    4 Uniqueness and Existence Theorems Appendix to §4. Extension of the Existence Theorem
    5 Solutions Containing Parameters
    PART B CONTINUATION OF SOLUTIONS. OTHER METHODS
    6 Continuation of Solutions
    7 Other Methods of Solution
  Chapter 2 Systems of Differential Equations
    Section 1 Introduction. Vector Notation
    2 Approximate Solutions
    3 The Lipschitz Conditions
    4 The Fundamental Inequality
    5 Existence and Properties of Solutions of the System
    6 Systems of Higher Order
  Chapter 3 Linear Systems of Differential Equations
    PART A THE GENERAL LINEAR SYSTEM
    Section 1 Introduction. Matrix Notation
    2 Linear Dependence. Fundamental Systems
    3 Solutions Expressed in Matrix Form
    4 Reduction of Order of a System
    5 Nonhomogeneous Systems
    PART B LINEAR EQUATIONS OF HIGHER ORDER
    6 Fundamental Systems
    7 The Wronsky Determinant
    8 Further Properties of the Fundamental System
    9 Reduction of Order
    10 The Nonhomogeneous Case
    11 Green's Function
    PART C LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS
    12 Introduction. Complex Solutions
    13 Characteristic Values and Vectors of a Matrix
    14 Vectors Associated with Characteristic Values of a Matrix
    15 The Solution in the Simplest Case
    16 The Solution in the General Case
    17 Homogeneous Equation of nth Order
    18 Applications
  Chapter 4 Singularities of an Autonomous System
    PART A INTRODUCTION
    Section 1 Characteristic Curves
    2 Isolated Singularities
    PART B SINGULARITIES OF A LINEAR SYSTEM
    3 General
    4 Nodal Points
    5 Saddle Points
    6 Degenerate Nodal Points
    7 Vortex Points
    8 Spiral Points
    9 Conclusion. Dynamical Interpretation
    PART C NONLINEAR SYSTEMS
    10 Introduction
    11 Nodal Points
    12 Saddle Points
    13 Spiral Points
    14 Indeterminate Cases
  Chapter 5 Solutions of an Autonomous System in the large
    Section 1 Introduction
    2 Geometrical Considerations
    3 Basic Lemmas
    4 Theorem of Poincare-Bendixson
    5 Poincare's Index
    6 Orbital Stability of Limit Cycles
    7 Index of Simple Singularities
  References
  Index

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