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An Introduction to Ordinary Differential Equations
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.
334 pages, Paperback
First published January 1, 2008
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Displaying 1 - 2 of 2 reviews
July 30, 2014
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.
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.
September 23, 2014
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.
Displaying 1 - 2 of 2 reviews