Ravi P. Agarwal,
Donal O'Regan
Springer New York
2008e druk, 2008
9780387712758
An Introduction to Ordinary Differential Equations
Specificaties
Paperback, 322 blz.
|
Engels
Springer New York |
2008e druk, 2008
ISBN13: 9780387712758
Rubricering
Onderdeel van serie
Universitext
Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.
Specificaties
ISBN13:9780387712758
Taal:Engels
Bindwijze:paperback
Aantal pagina's:322
Uitgever:Springer New York
Druk:2008
Serie:Universitext
Inhoudsopgave
Preface.- 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.- 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’s Direct Method for Autonomous Systems.- Lyapunov’s Direct Method for Non–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.- Sturm–Liouville Problems (Contd.).- Eigenfunction Expansions.- Eigenfunction Expansions (Contd.).- Nonlinear Boundary Value Problems.- Nonlinear Boundary Value Problems (Contd.).- Topics for Further Studies.- References.- Index