An Introduction to Ordinary Differential Equations

by Ravi P Agarwal . Donal O'regan

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 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.).

Paperback

First published January 1, 2008

Reviews

[Qubitng · Rating 4 out of 5]

Covers analytical techniques for solving single equation ODEs and some PDEs and is organized as 50 lectures. Each lecture is carefully written so it can be comfortably read in one sitting. This is a good book for anyone who has already taken a one semester undergrad course on differential equations. The book claims all you need is calculus, but this claim is completely unrealistic as the authors skim through the contents of a differential equations course all in the first 46 pages!

This sentence in the preface pretty much indicates who the intended audience is: "Like any other mathematical book, it does contain some theorems and their proofs". LOL. And true there aren't many theorems and of those theorems that are stated a good portion lack a proof. This book doesn't cover numerical methods nor uses anything requiring knowledge of linear algebra (eg, inner products and norms are used but you don't need to know what a vector space is). What is covered include series solutions, various special functions, Green's function, perturbation techniques, boundary value/Sturm Liouville, and solving PDEs centered around seperation of variables technique. Many exercises and hints/answers at the end of each chapter.

There is one thing I really don't like about this book: If you aren't going to prove a major theorem, at least give a reference or have a section in the chapter for "further reading". All we get are statements along the lines of "the reason is beyond the scope of this book" or "this is too difficult to cover here" or "this requires advanced concepts"; no elaboration, no reference.

3 stars + 1 star (pedagogical value of dividing the book into small lectures) = 4 stars.

[Dmitri · Rating 4 out of 5]

A very manageable and easy to read book on ODEs, recommended after reading a simpler text on DEs. This is what makes the Universitext series so good.