An Introduction to Ordinary Differential Equations (Dover Books on Advanced Mathematics)

It begins with a chapter covering the necessary background to understand the material, and then proceeds to study the first order linear equation. The next step is the 2nd order linear equation and then the n-th order linear equation. The most appreciated feature of this book is that the author shows that the method (an explicit formula!) for solving the n-th order equation is essentially the same as the 1st order one. After solving completely the linear equation the author moves on to the non-linear case, again up to the n-th order. The idea seems quite simple, yet no other customary text introduces ODE's this way. All the other authors begin with the 1st order equation mixing up the linear and the non-linear cases, and continue their exposition following the same fashion, leading the student to misunderstand a very subtle and important feature of analysis (and mathematics): the great difference between linearity and non-linearity. The way this book is written shows clearly this crucial phenomenon.

Another valuable feature of this book is its complex-number approach which leads to straightforward computation of explicit formulas for the solutions of linear equations. Other texts give no more than the sketch of some methods which have to be performed every single time, and most of them don't even justify those methods rigorously.

Conclusion: Superb book. Excellent as a course text.

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A great Introduction or review.   December 21, 2002
17 out of 17 found this review helpful

I took an undergraduate ordinary differential equations class and felt I grasped the subject quite well. I wanted an inexpensive text that I could review the subject with and I decided that I would give Coddington's book a try. I was really pleased with the order in which the text was presented which differed from the course I had taken. The author's seem to put things in a very logical order versus some texts I have seen which really confuse you by the order in which the subjects are presented. Another point that I have to make is the depth that the book has. I learned much more in reviewing this text than I ever did in any diff eq class. It shows the distinction between linear and non-linear diff eq's and covered many other methods which I had not learned previously. This is a great text as a "refresher" or as a course text. I just wish I would have previously used this text to learn ordinary differential equations.


excellent book   March 2, 2006
Tomas Selnekovic (Bratislava, SLOVAKIA)
8 out of 8 found this review helpful

I think this is one of the best books on the subject. If you really want to understand differential equations then you have to read an analysis book like this. The numerical recipes/methods books will teach you only how to program the computer to solve the the equations. This one will teach you WHY it works.


Holy Bible for Introduction to differential equations UG   December 8, 2002
15 out of 18 found this review helpful

This book is a holy bible for introduction to differential equations. It is easy to understand and the problems are quite challenging. Dr Coddington knows how to explain the material by systematically order(Easy to tough). His book is not easy to figure out if you just sit without paper,pen and think. But once you are understand his book, no one can teach you differential equations for undergarduate level. Other suggested reading are Theory of ordinary differential equations, Linear ordinary differential equations by Earl Coddington(Both of them), Ordinary Differential Equations by Fritz John,and Ordinary Differential Equations by Edward L Ince. Once the most important statement is: YOU KNOW DIFFERENTIAL EQUATIONS IF YOU UNDERSTAND WHAT IS GOING ON IN CODDINGTON'S AND FRITZ JOHN BOOKS.


better than most   May 6, 2007
Oscar R. Moll Thomae
2 out of 2 found this review helpful

I found this book relatively rigorous and concise. Good background for it would be some real analysis, but if you did calculus from something like Apostol or any other book that emphasizes proving statements then this still follows nicely. It may not cover all what a standard ODEs course covers, though, for example numerical methods for solving ODEs, transform techniques and systems of equations are not talked about.