An Introduction to Ordinary Differential Equations

Historical Notes.- Exact Equations.- Elementary First-Order Equations.- First-Order Linear Equations.- Second-Order Linera Equations.- Preliminaries to Existence and Uniqueness of Solutions.- Picard#x0027;s Method of Successive Approximations.- Existence Theorems.- Uniqueness Theorems.- Differential Inequalities.- Continuous Dependence on Initial Conditions.- Preliminary Results from Algebra and Analysis.- Preliminary Results from Algebra and Analysis (Contd.).- Existence and Uniqueness of Solutions of Systems.- Existence and Uniqueness of Solutions of Systems (Contd.).- General Properties of Linear Systems.- Fundamental Matrix Solution.- Systems with Constant Coefficients.- Periodic Linear Systems.- Asymptotic Behavior of Solutions of Linear Systems.- Asymptotic Behavior of Solutions of Linear Systems (Contd.).- Preliminaries to Stability of Solutions.- Stability of Quasi-Linear Systems.- Two-Dimensional Autonomous Systems.- Two-Dimensional Autonomous Systems (Contd.).- Limit Cycles and Periodic Solutions.- Lyapunov#x0027;s Direct Method for Autonomous Systems.- Lyapunov#x0027;s Direct Method for Nonautonomous Systems.- Higher-Order Exact and Adjoint Equations.- Oscillatory Equations.- Linear Boundary Value Problems.- Green#x0027;s Functions.- Degenerate Linear Boundary Value Problems.- Maximum Principles.- Sturm#x2014;Liouville Problems.- Sturm#x2013;Liouville Problems (Contd.).- Eigenfunction Expansions.- Eigenfunction Expansions (Contd.).- Nonlinear Boundary Value Problems.- Nonlinear Boundary Value Problems (Contd.).- Topics for Further Studies.

From the reviews:"Presents a thorough treatment of the classical material traditionally covered in an advanced book on ordinary differential equations, including a number of interesting historical notes. … The authors also discuss Lyapunov functions, Green’s functions comparison and separation theorems, maximum principle, Sturm-Liouville problems, Fredholm alternative, and Floquet theory. In addition, the book addresses results by Perron, Kamke, Osgood, Nagumo, Krasnoselski-Krein, and Van Kampen which are not found in some similar works. … Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers, and faculty." (J. D. Fehribach, Choice, Vol. 46 (8), April, 2009)"The textbook is devoted to a systematic and rigorous introduction to the theory of ordinary differential equations. … the practical part include numerous exercises with answers or hints. Written by two prolific leaders in the field of ordinary differential equations and nonlinear analysis, the textbook provides a very clear, well-organized and lucid introduction to ordinary differential equations, with an implicit orientation towards the most recent research topics and methods in the field and related areas." (Radu Precup, Zentralblatt MATH, Vol. 1158, 2009)“This text book provides an excellent introduction to the subject accessible to second-year undergraduate or graduate-level students. Its structure in the form of a succession of 42 class-tested lectures makes it not only an inspiring source for self-study but gives also a good framework for the organization of course material. … a highly recommendable book for students in mathematics, sciences, or engineering as well as for teachers on college and university level.” (G. Hörmann, Monatshefte für Mathematik, Vol. 159 (4), March, 2010)