Description
Book SynopsisThis important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
Table of ContentsQualitative theory - two-dimensional linear systems; two-dimensional almost linear systems; existence and non-existence of periodic solutions; Floquet's theorem; perturbation methods -regular and singular perturbation; method of multiple scales; method of averaging; matched asymptotic expansions; stability -definitions; Liapunov's direct method - autonomous system; Liapunov's direct methods - non-autonomous system; hydrodynamic stability; bifurcation and catastrophe - examples of bifurcation in one dimension; two-dimensional problems; discrete systems; elementary catastrophe; chaos - criteria for chaos; routes to chaos.
