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Publisher:

Dover Publications

Publication Date:

2002

Number of Pages:

144

Format:

Paperback

Price:

12.95

ISBN:

9780486664200

Category:

Textbook

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

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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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