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An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) [Unabridged] [Paperback]

Earl A. Coddington , Mathematics
4.2 out of 5 stars  See all reviews (20 customer reviews)

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Book Description

March 1, 1989 0486659429 978-0486659428 Unabridged
"Written in an admirably cleancut and economical style." — Mathematical Reviews.
This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented.
The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations.
Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems.

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An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) + Ordinary Differential Equations (Dover Books on Mathematics) + Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics)
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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: 4.2 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #67,250 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
96 of 97 people found the following review helpful
5.0 out of 5 stars Superb introduction to ODE's 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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48 of 48 people found the following review helpful
4.0 out of 5 stars One of the Better ODE Texts 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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42 of 42 people found the following review helpful
5.0 out of 5 stars A great Introduction or review. 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
5.0 out of 5 stars excellent book 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
4.0 out of 5 stars Concise, well written 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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40 of 52 people found the following review helpful
4.0 out of 5 stars An excellent text ... in 1970, not in 2003 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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Most Recent Customer Reviews
2.0 out of 5 stars Difficult to read.
This book is very hard to follow. I think the book was only a couple of bucks so I thought what the heck, it's worth a try.
Published 1 month ago by Bill
5.0 out of 5 stars classical
it's a classic in math theory, totally worth it to have in your shelf, no one should avoid reading it
Published 3 months ago by Gustavo S. Cortes
3.0 out of 5 stars Could be deeper
Not a bad book. I just don't like differential equations. This book was written at too low of a level for the course I took and I often found myself wanting more out of the... Read more
Published 7 months ago by dclark
5.0 out of 5 stars In excellent condition
I cannot provide a review based on the content of the book because I would have to do it after I finish reading my calculus books, something that is going to take a long time. Read more
Published 8 months ago by hector
5.0 out of 5 stars excellent introductory text
This is not only a superb introduction to ODEs, it is also a masterfully written math text, which is (unfortunately) very rare. Read more
Published 15 months ago by shma
2.0 out of 5 stars all proof no Examples
Its hard to understand a book when all it gives is proof on how something is instead of giving a couple of example problems
Published 15 months ago by W. Lopez
5.0 out of 5 stars Excellent Service!!! Product arrived on time!!! Keep-up the good...
Excellent Service!!! Product arrived on time!!! Keep-up the good work!!!Excellent Service!!! Product arrived on time!!! Keep-up the good work!!!Excellent Service!!! Read more
Published 17 months ago by Gerjack
5.0 out of 5 stars Great book
The text is easy to follow and very clear. My son attends a private catholic university and this purchase saved him a lot of money.
Published 18 months ago by Dawn Gotliebowski
5.0 out of 5 stars Quality
New book delivered quickly. Very good price on it.
With that said I would recommend this book for people with already a general understanding of differential equations. Read more
Published 18 months ago by Eric
4.0 out of 5 stars A good, demanding book
One of the plusses is that it involves complex-valued functionsof real variable from the start. This is not a cook-book approach. Read more
Published 18 months ago by George F. Feissner
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