worth the low dover price with the following warnings... | Ordinary Differential Equations

My own little opinion on this great book | Ordinary Differential Equations | Morris Tenenbaum, Harry Pollard

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	• Ordinary Differential Equations Morris Tenenbaum, Harry Pollard Dover Publications, 1985 - 818 pages average customer review:based on 39 reviews view larger image
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highly recommended

Overall not bad

This product was here much earlier than expected. It's an ok text, not the best I have ever seen. It' not too complicated to follow but I find the biggest problem is keeping my page while am trying to do questions. It is very thick but has a small cover and its hard to keep open and work in at the same time. Yet there are lots of examples to look at for guidance and if you into this kinda thing- answers so you can check yours, unlike "An Introduction to Ordinary Differential Equations" by Robinson.

worth the low dover price with the following warnings...

I have had this book in my collection for over 20 years and it is a very good book on
ODE's. The authors really do go out of their way to define every term, provide a number of good examples, not skip too may steps in their derivations, and try to hold the hand of the reader as much as possible.

So why do I not automatically give this book 5 stars like most everyone else ?

The main reason is that this book was originally written in the 1960's and the content is very old fashioned.
The chapter on numerical methods is very out of date. I feel this is the most important topic as most ODE's arising in practice have no closed form solutions and must be solved numerically.
The presentation also takes too much time to get going as much background/pre-req material is covered. Modern
qualitative techniques (e.g. see the book by Strogatz) are not covered and this is a very important topic in practice to gain
insights into nonlinear systems.
Laplace transforms should
be covered sooner in the book - engineers use Laplace Transfroms to solve linear constant coefficient ODE's and this is probably
the most important analytical technique in practice. Instead the book dwells on the D-operator approach which is
an ad-hoc way of performing calculations that should be performed using the Laplace Transformation.
A first course in ODE's should cover numerical methods in place of series solutions and this book spends alot of time
discussing series solutions. If you
have to deal with special functions such as Bessel take up the study of series solutions then.

I am not surprised that most students really like this book. The older books in calculus and ODE's really
do blow away all the full color, 4.5lb, glossy coloring-book style texts that are mass produced today. If you
like this book check out a solid old calculus book (e.g., 2nd edition of Schwartz, the 2 volume set by
Fobes, the 3rd alternate edition of Thomas, or the excellent book by Moise)

Another issue I have is that
I do not see how a student would come away from this book seeing the "beauty" of ODE's. Perhaps this is too much to ask for, but other books such as the ones by Martin Braun and George Simmons really did motivate me to become an engineer and take further courses in dynamical systems. I cannot say the same for this text.

In summary, this book is well worth the low dover price. It covers the basics well and is written for the student.
It is a blue collar math text (not out to impress but to teach) and is surely a good stand alone text or supplement to another text.
However I cannot say this is the best book on the subject as it does not provide a modern treatment of numerical methods
and does not, in my opinion at least, do a great job of fostering love and appreciation for the subject matter.

Overall rating = 3.75 stars

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My own little opinion on this great book

I took ODE this semester, and I was liking the subject until I got to read the textbooks assigned to it. It is impressive how the world is filled with giant text books that are absolutely dull and useless and extremely expensive. Luckly I have always been fond of Amazon, so I searched "Ordinary Differential Equations" and came upon this book, which at first glance looks tiny and unpromising, but trust me, this little beast doesn't only talk about ODE, it takes the subject, makes it its own, and in the most elegant of fashions transmits the knowledge so well that it even if I live in Ecuador and English is only my second language, I could grasp all what was necessary to, not only pass ODE, but to take my knowledge and apply it to computer programming right away.

Trust me, if a book teaches so well that you can go ahead and apply it just like that, it is something special.

Now strictly speaking on it's qualities:

First, the book is a breeze to read, you will not find yourself reading back again through the text because of the lack of good pedagogy, but be aware, the writer does not bother to make you laugh either (a quality most serious books should not have, but I like what Stephen Prata did on C++ Primer Plus). Secondly, Ordinary Differential Equations has all that you will probably need for the subject. Check the MIT Open Course Ware, I downloaded the exams on the web page and did them singlehandedly, only with what this book taught me. Actually, you'll see lots of other topics that MIT doesn't even cover, for example it has a very interesting section on numerical methods.

Something that has to be mentioned is that this book covers a great amount of material in a excellent order and pace. The writer never assumes that you are a genius on calculus, so he always makes sure to guide you, holding your hand on each topic, repeating theorems already mentioned to refresh your head, not skipping to many steps when solving examples. This feature is seen at it's best in the Series Methods section of the book. Also, the amount of problems is wonderful, they all have solutions and are right next to the problems, unlike the convention, which gives solutions only to the odd number problems and has them written at the very end of the book, something that I hate, for the constant page turning greatly damages the book. Don't you worry, the writer solves many examples and each subject, explaining everything so you can work on the problem set rather easily.

The only setbacks that I noticed on this book are that, when teaching the prerequisites to a subject, it doesn't bother to demonstrate the theorems (which is fine by me, because you should already know that stuff in the fist place), and it doesn't have all the fancy graphics that the outrageously expensive ODE books have (for this I use Matlab or Mathematica, so I also don't care about his). You also have to consider that his books is quite old, and the numerical methods are a bit dated, still, any good teacher will fill you in with the little updates made to the subject.

All in all this book is nothing short of amazing, I give it all my fingers up to anyone who is taking ODE or wants an awesome reference book. I found it easy to read, precise, and vast. This book will probably do you more justice than anything worth >$100.

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Ordinary Differential Equations

This is a great reference book covers a wide range of the basics of differential equations and techniques in solving them and lots of examples and problems.

Fundamental text on differential equations field

I used this text on my Differential Equations class. It was extremely usefull. It is extremely clear and exact when it defines and explains first and second order ODE's. Its major advantages are the wide varitey of problems and exercices in this topic. It contains at least two chapters that deal with problems of all complexity, including the field of Mechanical and Electrical Engineering. The topic of systems of ODE's is not treated with Linear Algebra fundamentals which is an important disadvantage at the moment of trying to generalize the case to greater systems and to give a formal explanation.

Another book that I used in my class was Elementary Differential Equations and Boundary Value Problems. It contains the clearness of the text commented but digs deeper on systems of ODE's and an introduction to Partial Differential Equations. Excelent text. Hope you make a good purchase!

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Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton?s Interpolation Formulas, more.

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