Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences

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.

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...

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!

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.

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.