|Number of Pages
Educational: Mathematics & numeracy
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.
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.
Table of Contents
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
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
Degenerate Linear Boundary Value Problems
Sturm-Liouville Problems (Contd.)
Eigenfunction Expansions (Contd.)
Nonlinear Boundary Value Problems
Nonlinear Boundary Value Problems (Contd.)
Topics for Further Studies