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

24 customer reviews
ISBN-13: 978-0486659428
ISBN-10: 0486659429
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 320 pages
  • Publisher: Dover Publications; Unabridged edition (March 1, 1989)
  • Language: English
  • ISBN-10: 0486659429
  • ISBN-13: 978-0486659428
  • Product Dimensions: 8.5 x 5.4 x 0.6 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (24 customer reviews)
  • Amazon Best Sellers Rank: #79,655 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

100 of 101 people found the following review helpful By Bernardo Vargas on April 3, 2000
Format: Paperback
This classic book appeared for the first time in the early 1960's, and the world is still waiting to see a better elementary text on ODE's.
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.
Please read my other reviews at my member page (click on my name above).
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49 of 49 people found the following review helpful By "gsibbery" on June 9, 2000
Format: Paperback
This book was used in my "Introduction to Ordinary Differential Equations" class when I was a senior at Louisiana State. I found it to be one of the better texts in differential equations that I have come across. The first chapter is mainly the prerequisite calculus, then the next chapter jumps into first order equations. Then unlike most other books, he jumps straight into second order problems. the biggest plus in the book is the ready use of complex analysis throughout, something which most books avoid altogether, thus allowing the student to get only a partial understanding of the theory needed to solve more advanced problems. Answers are included at the back of the book, problems are clear and well-explained, and there are enough advanced topics covered later in the book (including celestial mechanics) to keep the course interesting for students of all kinds.
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43 of 43 people found the following review helpful By UTFLY on December 21, 2002
Format: Paperback
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.
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21 of 21 people found the following review helpful By Tomas Selnekovic on March 2, 2006
Format: Paperback
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.
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18 of 19 people found the following review helpful By Another Reviewer on April 4, 2008
Format: Paperback Verified Purchase
I think that this book is excellent as a textbook for an Ordinary Differential Equations class. There are plenty of "compute-the-solution" exercises, but there are also a large amount of theoretical exercises. The book is very concise, but it is still legible. It is also very cheap, so students won't mind buying it :)

I think that this book also works well when not used as a textbook. If you are using this to learn ODE's by yourself, you really need to do some of the exercises since they are essential to the book. I do think that it is $11 well spent, since it teaches all of the basics of ODE's.

In terms of the topics covered, here they are:

- Linear, homogeneous, nth-order equations with constant coefficients.
- Linear, homogeneous, 1st and 2nd order equations with non-constant coefficients.
- Linear, non-homogeneous, nth-order equations with constant coefficients.
- Lienar, non-homogeneous, 1st and 2nd order equations with non-constant coefficients.
- Solutions to ODEs with regular singular points.
- Series solutions.
- Existence and uniqueness to linear equations.
- Non-linear first order equations.
- Existence and uniqueness to first order equations.
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43 of 56 people found the following review helpful By G. Cantor on October 15, 2003
Format: Paperback
I used this text as a reference over 25 years ago and it was great, for its time. Today, however, there are a number of books available with a more "modern" treatment - ones more likely to provide a more realistic view of the subject matter.
Arguably, ODE is a geometry course in disguise and not a collection of "party tricks" as it is often portrayed in older texts. Analytical methods are clean and easy to convey in the classroom but, frankly, they never appear in the "real world".
If you plan to (or do) encounter ODE's in your chosen field you'd do better to spend lots of time looking at qualitative and numerical techniques, i.e., a more up to date approach.
Coddington did a great job with the subtopics he did address but in the late sixties it would have been difficult, if not impossible, to really provide the reader with a solid feel for the depth and breadth of the subject.
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An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)
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