Ordinary Differential Equations

Ordinary Differential Equations. Existence, uniqueness, stability, and qualitative theory of ODEs. The literature on ordinary differential equations divides naturally along several axes: the foundational structures that organise the subject, the techniques that drive proofs and computations, the questions about classification or representation that animate current research, and the bridges to neighbouring areas of mathematics and science. The references below trace those axes through the canonical textbook treatments and recent technical contributions.

Foundations and canonical references

The standard treatments of ordinary differential equations approach the subject from complementary angles. Arnold, Ordinary Differential Equations (1992) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Tenenbaum, Ordinary Differential Equations (1985) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques. Hirsch, Differential Equations, Dynamical Systems, and an Introduction to Chaos (2012) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for ordinary differential equations include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.