Ordinary differential equations: a graduate text

ORDINARY DIFFERENTIAL EQUATIONS: A Graduate Text presents a systematic and comprehensive introduction to ODEs for graduate and postgraduate students. The systematic organized text on differential inequalities, Gronwall's inequality, Nagumo's theorems, Osgood's criteria and applications of different equations of first order is dealt with in a greater depth. The book discusses qualitative and quantitative aspects of the Strum - Liouville problems, Green's function, integral equations, Laplace transform and is supported by a number of worked-out examples in each lesson to make the concepts clear. A lot of stress on stability theory is laid down, especially on Lyapunov and Poincare stability theory. A numerous figures in various lessons (in particular lessons dealing with stability theory) have been added to clarify the key concepts in DE theory. Nonlinear oscillation in conservative systems and Hamiltonian systems highlights basic nature of the systems considered. Perturbation techniques lesson deals in fairly details to understand basic nature and approximate solutions of nonlinear DEs like: Rayleigh equation, Duffing equation, Lienard equation, van der Pol equation. KEY FEATURES: Contains over 596 worked out examples and over 569 unsolved (many with answers or hints) in the book Good bibliography and appendices Can be used as a reference after the students have completed learning elementary part of the subject