Recommended literature
Basic topics (existence and uniqueness of solutions, maximal solutions, linear equations, matrix exponential, continuous dependence on initial values, the first integral, stability, Floquet theory) are covered by most of the ''general books'' on ODEs (see the list below).
The best book for beginners in the is [Vra]; also [Gra] and [SchTho] are quite accesible.
More difficult to read are [Kur], [Chi] or [Arn], completely exhausting is then [Har].
Concerning more advanced topics (see also ``specialized books`` below):
- Carathéodory theory: [Kur].
- Dynamical systems: [Gra], [SchTho], [Kur].
- Theorem of Hartman and Grobman, center manifolds: [Har], [Gra], [Kur].
- Hopf bifurcation: [Chi], [SchTho],
- Optimal control: [Eva].
- Poincaré-Bendixson theory: [Gra], [Chi], [Har], [Kur].
- Sturm-Liouville theory: [Har], [SchTho].
General books
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[Arn]
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Vladimir I. Arnold: Ordinary differential equations. Springer 1992.
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[Gra]
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Christopher Grant: Lecture Notes on Ordinary Differential Equations.
(to download
here)
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[Har]
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Philip Hartman: Ordinary differential equations. SIAM 2004.
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[Chi]
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Carmen Chicone: Ordinary differential equations with applications. Springer 2006.
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[Kur]
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Jaroslav Kurzweil: Introduction to the Theory of Ordinary Differential Equations in the Real Domain, Elsevier, 1986
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[SchTho]
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Klaus Schmitt, Rusell C. Thompsson: Nonlinear Analysis and Differential Equations: An Introduction.
(to download
here)
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[Vra]
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Ioan I. Vrabie: Differential equations : an introduction to basic concepts, results, and applications. World Scientific, 2004.
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Specialized books
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[Car]
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Jack Carr: Applications of centre manifold theory. Springer 1981.
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[Eva]
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Laurence C. Evans: An Introduction to Mathematical Optimal Control Theory.
(to download
here)
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[HalKoc]
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Jack K. Hale, Huseyin Kocak: Dynamics and bifurcations. Springer 1991.
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