Ordinary Differential Equations (Dover Books on Mathematics)
by Harry Pollard, Mathematics, Morris Tenenbaum
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Book Summary Information
Author: Harry Pollard, Mathematics, Morris TenenbaumEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1985-10-01
ISBN: 0486649407
Number of pages: 818
Publisher: Dover Publications
Book Reviews of Ordinary Differential Equations (Dover Books on Mathematics)
Book Review: worth the low dover price with the following warnings...
Summary: 3 Stars
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The chapter on numerical methods is very out of date.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
Summary of Ordinary Differential Equations (Dover Books on Mathematics)
Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the 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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