Ordinary Differential Equations

Rating:
Summary: Very useful for theoretical physicists
Review: Readable, has a simple chapter on continuous groups that (implicitly) introduces the notion of global integrability. Discusses and uses Fuch's theorem (classification of singularities of linear ode's, basis for 'guessing' the right form of the series solution in terms of singilarities of coefficients), easy group theoretic discussion of singularities in the complex plane. Stage 2: see Arnol'd's Ordinary Differential Equations for theory, Bender and Orszag for approximation methods.

Rating:
Summary: An essential reference work for anyone working in ode's
Review: This classic (originally published in 1926 and still in print!) combines readability with a vast wealth accurately presented material (much of which can still only be found in research papers and certainly can nowhere else be found in a single reference). Most astpects of theory are illustrated by examples.

The main areas covered in the book are existence theorems, transformation group (Lie group) methods of solution, linear systems of equations, boundary eigenvalue problems, nature and methods of solution of regular, singular and nonlinear equation in the complex plane, Green's functions for complex equations.

This is an essential reference for anyone working with ordinary differential equations.