دانلود کتاب Lectures on advanced ordinary differential equations

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Title page
Chapter I. Invariant Differential Equations. Lie\'s Theory
1. Introductory Remarks
2. Transformations
3. Transformation of Functions
4. Transformation of a Set of Curves
5. Transformation of a Direction Field
6. Differential Equations Invariant under Given Transformation
7. Lie\'s Integrating Factor
8. Infinitesimal Transformations
Chapter II. Existence and Uniqueness
1. Preliminary Remarks
2. Metrization
3. Integral Operation
4. Convergence of Iterations
5. Application to Differential Equations
6. Dependence of Solutions on Initial Values or Other Parameters
7. Remarks about Other Existence Theorems
8. Remarks about the Domain of Existence
9. Remarks about the Existence of Periodic Solutions
10. Remarks about Systems of Equations
11. Linear Differential Equations
Chapter III. Discussion of the Topology of Integral Curves
1. Singularities
2. Linear Differential Equations
3. Path Curves near a Singular Point: Geometrical Discussion
4. Existence of the Exceptional Integral Curve through a Singular Point
5. Integral Curves in the Large. Closed Integral Curves
6. Number and Type of Singular Points
Chapter IV. Periodic Solutions of Differential Equations
1. Analytic Determination of Periodic Solutions
2. The Variational Equation
3. Holonomic Differential Equations
4. The Degenerate Problem
5. The TotaIly Degenerate Problem
6. The Bifurcation Problem for Equations of Second Order
7. A Modifted Implicit Function Theorem
8. Solution of the Degenerate Problem and of Related Problems
9. Remarks about Linear Differential Equations with Periodic Coefficients
Appendix to Chapters II, III, IV
1. Remarks about the Manifold of all Solutions of a Linear Differential Equation with Constant Coefficients
2. Remarks about the Stability Problem
Chapter V. Linear Differential Equations for Analytic Functions
1. Introduction
2. Existence, Uniqueness, Circuits
3. Circuits
4. Regular Singularities
5. The Nature of the Proper and the Generalized Eigen-Solutions of a Differential Equation with a Regular Singularity
6. The Non-homogeneous Equation
7. An Equation of the nth Order for One Unknown Function
8. The Hypergeometric Functions
9. Integral Representation of the Hypergeometric Function
10. Singular Singularities. Pseudo-regular Differential Equations
11. Existence of a Pseudo-regular Solution
12. Asymptotic Expansion
13. Recessive and Dominant Solutions. Stokes Phenomenon
14. Asymptotic Expansion with Respect to a Parameter
15. Circuit Transformation of the Asymptotic Expansion with Respect to a Parameter
Index