Basic Theory of Ordinary Differential Equations

1. Front Matter

   Pages i-xi

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2. Fundamental Theorems of Ordinary Differential Equations

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 1-27

3. Dependence on Data

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 28-40

4. Nonuniqueness

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 41-68

5. General Theory of Linear Systems

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 69-107

6. Singularities of the First Kind

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 108-143

7. Boundary-Value Problems of Linear Differential Equations of the Second-Order

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 144-196

8. Asymptotic Behavior of Solutions of Linear Systems

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 197-234

9. Stability

   • Po-Fang Hsieh, Yasutaka Sibuya

   Pages 235-278

10. Autonomous Systems

    • Po-Fang Hsieh, Yasutaka Sibuya

    Pages 279-303

11. The Second-Order Differential Equation \(\frac{{{{d}^{2}}x}}{{d{{t}^{2}}}} + h\left( x \right)\frac{{dx}}{{dt}} + g\left( x \right) = 0\)

    • Po-Fang Hsieh, Yasutaka Sibuya

    Pages 304-341

12. Asymptotic Expansions

    • Po-Fang Hsieh, Yasutaka Sibuya

    Pages 342-371

13. Asymptotic Solutions in a Parameter

    • Po-Fang Hsieh, Yasutaka Sibuya

    Pages 372-402

14. Singularities of the Second Kind

    • Po-Fang Hsieh, Yasutaka Sibuya

    Pages 403-452

15. Back Matter

    Pages 453-469

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The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a variety of different fields. The text is suitable for a one-year graduate course, as well as a reference book for research mathematicians. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history. The book has 114 illustrations and 206 exercises. Hints and comments for many problems are given.

• Differential operator
• Eigenvalue
• Ordinary Differential Equations
• Smooth function
• differential equation
• maximum
• minimum
• ordinary differential equation

"This book in pure mathematics will guide the reader on a newly marked path through classic and awesome terrain---first so well described by Coddington and Levinson---toward research in the important and useful areas of power series solutions and asymptotics. The path not taken would be marked by at least one explicit mention of a Poincaré map, a resonance in celestial mechanics, an average, a traveling wave, or a transversal intersection of separatrices."--MATHEMATICAL REVIEWS

• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, USA

  Po-Fang Hsieh

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Yasutaka Sibuya

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