Author | Walter, Wolfgang. author |
---|---|
Title | Ordinary Differential Equations [electronic resource] / by Wolfgang Walter |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0601-9 |
Descript | XI, 384 p. online resource |
I. First Order Equations: Some Integrable Cases -- ยง 1. Explicit First Order Equations -- ยง 2. The Linear Differential Equation. Related Equations -- ยง 3. Differential Equations for Families of Curves. Exact Equations -- ยง 4. Implicit First Order Differential Equations -- II: Theory of First Order Differential Equations -- ยง 5. Tools from Functional Analysis -- ยง 6. An Existence and Uniqueness Theorem -- ยง 7. The Peano Existence Theorem -- ยง 8. Complex Differential Equations. Power Series Expansions -- ยง 9. Upper and Lower Solutions. Maximal and Minimal Integrals -- III: First Order Systems. Equations of Higher Order -- ยง 10. The Initial Value Problem for a System of First Order -- ยง 11. Initial Value Problems for Equations of Higher Order -- ยง 12. Continuous Dependence of Solutions -- ยง 13. Dependence of Solutions on Initial Values and Parameters -- IV: Linear Differential Equations -- ยง 14. Linear Systems -- ยง 15. Homogeneous Linear Systems -- ยง 16. Inhomogeneous Systems -- ยง 17. Systems with Constant Coefficients -- ยง 18. Matrix Functions. Inhomogeneous Systems -- ยง 19. Linear Differential Equations of Order n -- ยง 20. Linear Equations of Order nwith Constant Coefficients -- V: Complex Linear Systems -- ยง 21. Homogeneous Linear Systems in the Regular Case -- ยง 22. Isolated Singularities -- ยง 23. Weakly Singular Points. Equations of Fuchsian Type -- ยง 24. Series Expansion of Solutions -- ยง 25. Second Order Linear Equations -- VI: Boundary Value and Eigenvalue Problems -- ยง 26. Boundary Value Problems -- ยง 27. The SturmโLiouville Eigenvalue Problem -- ยง 28. Compact Self-Adjoint Operators in Hilbert Space -- VII: Stability and Asymptotic Behavior -- ยง 29. Stability -- ยง 30. The Method of Lyapunov -- A. Topology -- B. Real Analysis -- C. C0111plex Analysis -- D. Functional Analysis -- Solutions and Hints for Selected Exercises -- Literature -- Notation