05497nam a22003975i 4500978-0-387-71276-5cr nn 008mamaa100301s2008 xxu: s :::: 0:eng d9780387712765DOI : 10.1007/978-0-387-71276-5ENGUS515.352Online Resource : SpringerAgarwal, Ravi P.An Introduction to Ordinary Differential EquationsEBby Ravi P. Agarwal, Donal O'Regan.New York, NYSpringer2008.online resource.textonline resourceUniversitextPreface -- Introduction -- Historical Notes -- Exact Equations -- Elementary First Order Equations -- First Order Linear Equations -- Second Order Linear Equations -- Preliminaries to Existence and Uniqueness of Solutions -- Picardâs 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 QuasiâLinear Systems -- TwoâDimensional Autonomous Systems -- TwoâDimensional Autonomous Systems (Contd.) -- Limit Cycles and Periodic Solutions -- Lyapunovâs Direct Method for Autonomous Systems -- Lyapunovâs Direct Method for NonâAutonomous Systems -- Higher Order Exact and Adjoint Equations -- Oscillatory Equations -- Linear Boundary Value Problems -- Greenâs Functions -- Degenerate Linear Boundary Value Problems -- Maximum Principles -- SturmâLiouville Problems -- SturmâLiouville Problems (Contd.) -- Eigenfunction Expansions -- Eigenfunction Expansions (Contd.) -- Nonlinear Boundary Value Problems -- Nonlinear Boundary Value Problems (Contd.) -- Topics for Further Studies -- References -- Index.This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines. Key Features of this textbook: Effectively organizes the subject into easily manageable sections in the form of 42 class-tested lectures Provides a theoretical treatment by organizing the material around theorems and proofs Uses detailed examples to drive the presentation Includes numerous exercise sets that encourage pursuing extensions of the material, each with an "answers or hints" section Covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics Provides excellent grounding and inspiration for future research contributions to the field of ODEs and related areas This book is ideal for a senior undergraduate or a graduate-level course on ordinary differential equations. Prerequisites include a course in calculus. Series: Universitext Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 800 journal articles and more than 20 books, and actively contributes to over 40 journals and book series in various capacities. Donal OâRegan received his Ph.D. in mathematics from Oregon State University, Oregon, U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is the author/co-author of 14 books and has published over 650 papers on fixed point theory, operator, integral, differential and difference equations. He serves on the editorial board of many mathematical journals. Previously, the authors have co-authored/co-edited the following books with Springer: Infinite Interval Problems for Differential, Difference and Integral Equations; Singular Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To V. Lakshmikanthan on his 80th Birthday. In addition, they have collaborated with others on the following titles: Positive Solutions of Differential, Difference and Integral Equations; Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations.Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).Mathematics.Differential Equations.Differential equations, PartialEngineering mathematics.Mathematics.Ordinary Differential Equations.Partial differential equationsAppl.Mathematics/Computational Methods of Engineering.O'Regan, Donal.author.SpringerLink (Online service)Universitexthttp://dx.doi.org/10.1007/978-0-387-71276-5