Arnol'd's ODE book distinguishes itself from the dozens of others by its emphasis on the qualitative and geometric theory rather than the quantitative theory. His aim is to analyze and describe the behavior of systems, rather than providing a collection of unexplained tricks for solving specific equations. Thus, there are plenty of examples and figures, but no complicated formulas. Arnol'd is known by mathematicians and students both for his mathematical skills and for his talent for mathematical writing.

Furthers the understanding of ODEs by using a geometrical interpretation Excellent for physics students, too One of the best textbooks of all times

Autorentext

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. His first mathematical work, which he did being a third-year student, was the solution of the 13th Hilbert problem about superpositions of continuous functions. His early work on KAM (Kolmogorov, Arnold, Moser) theory solved some of the outstanding problems of mechanics that grew out of fundamental questions raised by Poincare and Birkhoff based on the discovery of complex motions in celestial mechanics. In particular, the discovery of invariant tori, their dynamical implications, and attendant resonance phenomena is regarded today as one of the deepest and most significant achievements in the mathematical sciences. Arnold has been the advisor to more than 60 PhD students, and is famous for his seminar which thrived on his ability to discover new and beautiful problems. He is known all over the world for his textbooks which include the classics Mathematical Methods of Classical Mechanics, and Ordinary Differential Equations, as well as the more recent Topological Methods m Hydrodynamics written together with Boris Khesin, and Lectures on Partial Differential Equations.

Inhalt
Basic Concepts.- Basic Theorems.- Linear Systems.- Proofs of the Main Theorems.- Differential Equations on Manifolds.