Customer Reviews

Differential Equations and Their Applications : An Introduction to Applied Mathematics (Texts in Applied Mathematics, Vol. 11)

5 star:		(9)
4 star:		(2)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

As an academic I rarely if ever use textbooks because I find their writing style bland and disengaging--especially in my own area (economics). Braun's text is the exception to the rule: this is a textbook that is so well written it could qualify as entertainment. At the same time the major issues in the field are covered well, complete with an overview of the linear algebra required for doing ODEs and a good introduction to nonlinearity and chaos. It may not, as one reviewer notes, provide a complete and rigorous coverage of this highly technical field, but it does what a text should do but so few achieve: it excites its readers and inspires them to delve further into this fascinating discipline.

This book covers its material thoroughly and clearly with the most interesting set of applications I've seen in a high-level text. It also contains all the linear algebra needed to understand the material. This book was based on a course the author taught. Indeed, Braun's claim that students taking linear algebra would refer to his course for a refresher is well-deserved. Exercises are generally difficult but the examples are easy to follow. Buy this if you want to truly understand the subject matter.

I have used this to teach DE's in a one to one tutoring context for a couple of years now, since I first picked it off a library shelf and felt literally like jumping for joy over how good it was. Not that I dislike Boyce / DiPrima, but suddenly I had a text that was really fun! Now, this is definitely a "what DE's are good for" kind of text, so if you feel that your students should suffer teething pains on a dry theoretical tome, this is NOT the book for you. Nevertheless, having had students chew up all their available time on this book, because they loved it, makes me recommend it highly.

This book is extraordinarily clear as well as being concise (but never too much so) in the mathematical parts. Discussion of applications is verbose, but is kept in separate sections; this material can be omitted entirely or read later without any detrimental effect to the flow of the book. However, the discussion of the applications is interesting and deep, and would be useful (and fun) for motivated students to read.

The book begins with a no-nonsense discussion of how to solve differential equations analytically. Unlike many books, it gives clear instructions to the reader as to how to know which techniques are applicable. Also, it does not introduce qualitative or numerical methods until it has already developed a number of analytic techniques, and in my opinion, this results in greater clarity than the path most books take of integrating (or should I say jumbling?) the material together. The book gradually and logically covers the ground between analytic and numerical, moving towards actually writing algorithms, which are included in the text. The emphasis is always on understanding. Exercises are straightforward and useful.

My only complaint is that, in this modern age, the C programs should be included in the text and the Pascal and FORTRAN ones relegated to the index. (It is the other way around, alas.)

This book is simply wonderful for anyone studying differential equations for the first time. I do not understand why undergraduate institutions use the more commercialized texts instead of ones like this. This is a great book; it would be excellent for a textbook or for self-study.

Goes every the mathematical details for the development of solution methods. Includes numerical methods as well. Many applications provided. Far superior to standard undergraduate texts in differential equations.

I like this book for its excellent examples of applications.Later chapters give intro to linear algebra and Laplace transforms and delta function in an easy manner.I learnt these advanced topics from this book.This is not an ordinary class text book, but a good supplementary one....needs wider advertising.

i am enrolled in a financial engineering masters program and we constantly come across a differential equations problem. Having never taken a class on odes or pdes, i thought i should get a good book to study on my own. and wow, this book is so well written that i feel pretty confident in my differential equations ability. good book and highly recommended..

This is the typical mathematics book intended for non-mathematicians. The author made a great effort to compile the most diverse examples of problems (better said MODELS of problems) that can be solved employing mostly ODE and some PDE techniques. However, I think this kind of books fail to show what mathematics is, and how mathematics should be used to solve problems coming from other fields of knowledge.

First, the book does not cover thoroughly the theory for the linear case, which could be carried out without any effort up to the n-th order. Second, it does not tell explicitly the great difference between the linear and the non-linear cases. Third, eventhough it includes some material on systems of differential equations, it doesn't exploit the fact that a n-th order equation can be viewed as a n-th order system of of 1st order equations. Fourth, everything is mixed up: in the same chapter you find elementary concepts of linear algebra (that the student should be supposed to master), some miscelaneous applications, and, if you are lucky, some theory on differential equations. Fifth, it gives a wrong idea of the meaning of solving an ACTUAL problem. The fact that we are able to give a nice solution to a highly simplified model we have built does not mean that we have found a practical solution to the problem we actually face up in the real world, and moreover it does not mean that we will always succeed to give a useful answer by employing these tools. When you try to solve a problem that you don't know thoroughly you take the risk of building castles in the air. I think that if you are interested in applying mathematics you should start first by learning all the necessary theory and then study carefully the problem you are interested in. And don't forget the most important of all: the theoretical solution to an actual problem must be confirmed by experimentation, something this book does not point out.

To tell something positive about it let me say that you will find a lot of challenging excercises, some of its "application" problems are interesting, and if you are a teacher it will serve well as a companion text for real treatises on differential equations like Coddington's or Kaplan's.

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I quite liked this book. It taught the material in a different order than I am used to, which gave me a more complete understanding. I would recommend it, especially to people who already know a bit about differential equations, as it is quite wordy and assumes some prior knowledge.

From a pedagogy point of view this is a bad book becuase of the way its chapters are organized and presented. There seems to be a lack of a natural order of topic in the book, specifically that theory and applications are intertwined/overlapped rather than placed in seperate chapters. Also, few exercises are presented at the end of a section.
Putting aside the pedagogy philosophy, this is a great book for a one semester course in Differential Equations but I would rather choose "Differential Equations, The Classic 5th edition" by Dennis G. Zill.