Customer Reviews

Ordinary Differential Equations (Dover Books on Mathematics)

5 star:		(40)
4 star:		(3)
3 star:		(3)
2 star:		(1)
1 star:		(0)

 

 

After going through this book and finishing a few weeks ago, and looking at some other comparable titles, I have to come to the conclusion that this is quite possibly overall the best introductory text on ODEs out there.

The book consists of six major subtopics: first-order equations, general nth-order linear equations, systems and nonlinear equations, series solution methods, numerical solution methods and existence/uniqueness theorems. Most of the subjects tend to be divided into two or three chapters, with the first one or two containing the theoretical aspect and computational techniques and the other consisting of applications to real world problems.

At some 800-odd pages the book is quite long, but the sheer amount of material covered is simply astounding; the book has several types of special ODEs and solution methods that I have not seen anywhere else, and the authors go to great lengths to make every concept fully clear to the reader while still being quite rigorous. I am personally somewhat pure-math oriented but also needed some practice with applied problems, and this text is sure to please both students of mathematics as well as those of the sciences due to the very large amounts of subject material contained in both areas. (the book is split about 55-45 in theory/application)

One very nice thing is that if there is some doubt as to whether or not the reader is comfortable with something from another subject (i.e. real analysis), the book does not assume that the reader is familiar wih that topic, but rather it goes through a short review of the topic that is self-contained enough for readers who have not heard of the topic before to get a good idea of it. There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. The numerical methods are also surprisingly robust considering that the book was written in 1963 and calculators/computers were not all that standard. Also, as was remarked earlier, this is one of the very few texts out there that contains the answers to all of the exercises, making it perfect for the self-study that I used it for; other authors/publishers should learn from this.

All things considered, this ranks among the best textbooks on any subject that I have ever seen, and coupled with the extremely low price, it definitely lies in the "must buy" category.

For math background, all that is needed for this book is a first semester in calculus. If you are looking for a book to learn ordinary differential equations (ODEs) from or for a second book for a class, buy this one. The book (which covers methods of solving/applying ordinary differential equations) are explained in just the right amount of detail--it isn't a novel, but it isn't something you should get too bogged down in. Also, there are LOTS of examples, which are all very helpful! The problem sets were put together very well--there are lots of problems and they start out easy and get harder. Also, one of the best things about this book is that it has most of the answers to problems! This makes this book more than sufficient for self-study. This is my favorite Dover Publications book!

Morris Tenenbaum and Harry Pollard's 1963 first-rate introduction to _Ordinary Differential Equations_ remains the superlative text on the market.

Compendious and catholic, the book contains 65 lessons organized into 12 chapters. The student learns method after method after method with comfort and ease. A typical lesson succinctly begins with explicatory material followed with completed examples. Each lesson ends with a problem set, and to the salvation of humanity, almost all of the answers are provided, making this book great for self-study, reference, and/or supplementation. A satisfactory calculus background should be the student's only necessary qualification; the involved calculus often demands more perspiration than the differential equations themselves. Those who repent shall receive redemption!

Included applications, while eating considerable space, can be found compartmentalized in separate chapters. For instance, chapter 3 contains applications involving 1st order differential equations, including topics like interest, dilution and accretion, decomposition and growth, temperature, pursuit curves, the flow of water, rotation of a liquid in a cylinder, et cetera. Chapter 6 does the same thing with second order differential equations, dealing with undamped and damped motion, electric circuits, planetary motion, suspension cables, y'get the idea.

Summarizing the more strictly mathematical content also presents itself as an impossible task. The book develops ideas concerning 1st order differential equations, second order differential equations, operators, Laplace transforms, the gamma function, the Bessel equation, the Legendre equation, the Laguerre equation, Wronskians, Picard's Method, series and numerical methods, perturbation method, all topped off at the end with existence and uniqueness theorems. And I've only scratched the surface! While the scope of the content of the book might initially intimidate, the presentation and development of the ideas consistently will be found faithfully friendly.

If one wants an enduring and everlasting introduction to differential equations, one has a sacred calling to purchase this +800-page bible. Amen.

I have had this book in my collection for over 25 years and it is a very good book on
ODE's. ( In fact , I have an original hardcover copy and like it better than the dover paperback reprint as it has larger font size and is easier to read.)
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.
Unlike calculus and advanced calculus where the techniques have not changed much in 50 years (see my further
comment below), computers
and nonlinear dynamics/chaos theory have really changed the way a course in introductory
differential equations should be taught.
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.
Modern
phase plane 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 or Hypergeometric take up the study of series solutions then.

The fact that most people really like this book is a special case of a more
general maxim which states that older textbooks are of superior quality compared to their modern counterparts.
For example, older books in calculus really
do blow away all the watered-down, full-color, 5lb, phone-book style texts that are mass produced today. If you
like Tenenbaum's text check out a solid old calculus book such as the 2nd edition of Schwartz or the
excellent text by Bers.

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 one by Martin Braun ("Differential Equations and Their Applications" which is now in its 4th edition)
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, although it is a very good book, 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 = 3.99 stars

This book is a must. For the undergrad, for the physicist, for the casual problem solver.

Just for fun, I did a Google search using "Ordinary Differential Equations" as search text. I just wanted to see how my favorite differential equations textbook rated some forty years after it was printed and forty years after I worked my way through it alone without an instructor. I expected no response. I was very surprised (and pleased) to see it come up as the first item in the list: Tenenbaum and Pollard. I own the Harper and Row first edition, first printing, dated March, 1964, that I purchased in Japan. It belongs number one! Five Solid Stars. Kudos to Dover for reprinting the book. Dover is an essential reprint resourse.

At the time I purchased the book, I was very interested in mathematics, engineering, and physics textbooks that one could read without the aid of an instructor as I was teaching myself mathematics, engineering, and physics without access to anyone who could field questions at this level. This is one of those very rare books that was written with the self taught student in mind, be it either accidental or intentional.

Mathematics is supposed to be fun. Most math text books are notoriously less than ideally written and tedious to read. When I studied differential equations in class at the university, the text was not too well written and the course content followed the text. Neither could touch this gem which I had previously worked my way through.

The examples are excellent and wide spectrum. They pull examples from all the many corners of physics, including everyday things pulled from the home that you do not give a second thought to.

Differential equations form an essential basis for my profession, and in general that is how I use them: for work. As I said, this book is also fun. For forty years, I have been opening my copy of this book randomly to any section and working whatever problem happened to be there. My last problem was a pursuit problem: deriving the trajectory of an airplane flying toward a destination city where cross winds were present. After I solved the problem, I went to Google...

This is definitively the best differential equations introduction book that I Know until this moment. Although there are other excellent books on this topic, this one has the particularity that for each one of the topics that tries, has a collection of carefully elected exercises for the author, in such a way that the student won't feel frustrated of finding exercises that don't have a direct content with the exposed theory, also ordered in upward difficult . Each chapter is divided in lessons where introduces step to step the elements that will serve later to understand some particular differential equation. With detail and accuracy, the only resource that is needed to know is how to integrate, the rest is in the book. The author doesn't consider that the reader knows something, it simply supposes that doesn't know it, and then it enriches the text with methodological explanations that make that the text is almost self contained, without for that reason, subtract depth in the topics. For my is a true pleasure to sit down to read this book, which I always learn on what should thinks when writing a book: think in the more general possible reader.

Harry Pollard was my professor for the second course in real analysis at Purdue in 1962 (he must have been writing this book then). He made differentials and manifolds crystal clear in the same easy way in which this book is written. Many authors belabor an 800 page text, and for some students this is overdone. However, if you want to get a genuine feel for ODE's as something more than a collection of techniques, you can profit highly from a leisurely but thorough tour through this book.

I read this book and it is one of the good ones. Yes it was published in 1960s but its totally fresh. It doesent use very old terminology or symbolism or anything. I get concerned about buying an old book, but for this price its a joke. I would easily pay $50 bucks for this because its solid. More text than math. Not a book chock full of equation explanations or diffucult and unproven "proofs." This book explains clearly each step and WHY! Explanations are real world examples not the "watch how cute the numbers look" examples of other books.

Definitely buy this book if you need a reference or are new to the subject.

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 too 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.

While working on a project that dealt with complex numbers and differential equations, I got Ordinary Differential Equations to aid me in my research for common sets of differential equations. Although the book did not help me with that purpose, I read the text and found that it was clearly written and organized in a very logical manner. Even with a mathematical background as weak as mine (I am a high school senior with only one year of calculus), this text is well worth owning due to its enormous potential as a reference and its ability to explain a very complex topic with such simplicity. If one is even remotely interested in learning about differential equations, with or without a solid mathematical background (although calculus, obviously, is needed), Ordinary Differential Equations is a great assest to anyone's mathematical library, and Dover publications, as usual, makes this text very affordable.