Buch, Englisch, 322 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1060 g
Reihe: Universitext
Buch, Englisch, 322 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1060 g
Reihe: Universitext
ISBN: 978-0-387-71275-8
Verlag: Springer
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 contains several key features. It 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 through interesting preliminary lectures. The rich array of topics covered allows for flexibility in developing the subject beyond the basics.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
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.
