An Introduction to Ordinary Differential Equations - Softcover

Softcover

ISBN 10: 8132206738 ISBN 13: 9788132206736

Publisher: Springer

Synopsis

Key Features 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. About the Book: An Introduction to Ordinary Differential Equations 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. Contents 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.).

Edition details

• Publisher: Springer
• ISBN 10: 8132206738
• ISBN 13: 9788132206736
• Binding: Paperback
• Language: English