Ordinary Differential Equations

Rating:
Summary: Very impressive...
Review: 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.

Rating:
Summary: Wow -- Perfect ODE book for an undergrad
Review: 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!

Rating:
Summary: Wow -- Perfect ODE book for an undergrad
Review: 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!

Rating:
Summary: WORTH MORE THAN MONEY
Review: 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.

Rating:
Summary: Good but not perfect
Review: Sure maybe you are a Math major then this book is a 5. But for us Physics/Engineering majors this book is a 4.

No Hardcover, No Solutions Manual, Format is bland, hard to write your own notes, and the physical quality is weak. More suited for a tom clancy novel than a Textbook.

All in all though if this were your only book in ODE...you would learn ODE well. Answers to most problems and good examples. Easy to follow. I think most of the problems areas are cause by the publisher trying to save money and lower the retail price than the author's ability to produce a quality text book. I hope the authors get picked up by Wiley or Adison-Wesley not a weak discount publisher like Dover.

Rating:
Summary: Fun with Differential Equations
Review: 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...


Rating:
Summary: Excellent...Very well written
Review: This is definitively the best introduction book to the differential equations 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 it introduces step to step the elements that will serve him later on in particular in the understanding of some differential equation. With detail and accuracy, the only resource that is needed is to know how to integrate, the rest is in the book. The author doesn't consider that the reader knows something, it simply supposes that he doesn't know it, and then it enriches the text with methodological explanations that make that the text is almost self contained, without for it, to subtract depth in the topics. It is for my a true pleasure to sit down to read this book, of which I always learn on what should be made when one thinks of writing a book: to think of the more general possible reader.

Rating:
Summary: Excellent!!!!!!!!
Review: This manual on ordinary differential equations is a classic in its own right. This manual obviously highlights the reality that education in general must have been superior in the past compared to the education of today. I assure anyone that decides to read this manual on ODE will understand ODE completely. I have not even seen people at M.I.T. be able to construct a manual of this quality.





Rating:
Summary: An excellent introduction to differential equations
Review: 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.