An introduction to ordinary differential equations - Agarwal, Ravi P.; O'Regan, Donal (New York, NY Springer Science + Business Media LLC, 2008)
This textbook provides a rigorous & lucid introduction to the theory of ordinary differential equations, which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.
Introduction -- Historical notes -- Exact equations -- Elementary first-order equations -- First-order linear equations -- Second-order linear equations -- Preliminaries to existence and uniqueness of solutions -- Picard's method of successive approximations -- Existence theorems -- Uniqueness theorems -- Differential inequalities -- Continuous dependence on initial conditions -- Preliminary results from algebra and analysis -- Existence and uniqueness of solutions of systems -- General properties of linear systems -- Fundamental matrix solution -- System with constant coefficients -- Periodic linear systems -- Asymptotic behavior of solutions of linear systems -- Preliminaries to stability of solutions -- Stability of Quasi-linear systems -- Two-dimensional autonomous systems -- Limit cycles and periodic solutions -- Lyapunov's direct method for autonomous systems -- Higher-order exact and adjoint equations -- Oscillatory equations -- Linear boundary value problems -- Green's functions -- Degenerate Linear boundary value problems -- Maximum principles -- Sturm-Liouville problems -- Eigenfunction expansions -- Nonlinear boundary value problems -- Topics for further studies.
Includes bibliographical references (pages [315]-317) and index.
Keywords: Differential equations