Differential Equations with Applications and Historical Notes

by George F. Simmons

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations―among others―as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author―a highly respected educator―advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity―i.e., identifying why and how mathematics is used―the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout.



























Outstanding Academic Title of the Year, Choice magazine, American Library Association.

Genres: Mathematics, Textbooks, Science, Reference, Physics, Calculus

762 pages, Paperback

First published January 1, 1972

About the author

George Simmons was an American mathematician who worked in topology and classical analysis. He was known as the author of widely used textbooks on university mathematics.

Reviews

[Vijayvamsi]

i havn't read yet.
How do i open it?

[Taka · Rating 4 out of 5]

Good!

I used this to complement Tenenbaum and Pollard's excellent textbook on the same topic, and though Simmons doesn't show every step of the proofs, the gaps are small enough that you can figure it out on your own after some careful thinking. But it is a bit annoying for sure. The problems are a lot harder—and instructive—than Tenenbaum & Pollard's and all the answers to the exercises are included at the end of the book, so I learned a lot from grappling with the problems (especially Bernoulli numbers/polynomials and their applications!). Some of Simmon's explanations worked better for me than Tenenbaum & Pollard's (like using one solution to find another and Frobenius series), so it was a good idea for me to learn from two textbooks on the same subject.

[Alexander Bos · Rating 4 out of 5]

Reviewing this book as someone who didn't have any prior exposure to ODEs.

I'm really leaning between a 3/4 star here. The book started out rough, where the first 3 paragraphs of chapter 1 were good, only to find out by other people's opinions on mathstackexchange that the other paragraphs of chapter 1 had exercises in them that are introduced way too early!
So I had to skip 3/6 paragraphs from the get go due to that.

The rest of the book was fine in that sense, though sometimes when I was reading, I couldn't help but feel as if I was reading a summary, rather than a textbook. The lack of theory is a bit too much, most of which are located in the appendices or the second to last chapter. It was very much about the formulas and knowing how to use them.

It reminds me of when I read a short collection of thoughts by Rota, in which he said that ODEs are taught the wrong way. It's almost like Calculus 2 class, with a bunch of tricks to find the solution of the ODEs, without explaining too much on why they're useful, if they even are useful in practical contexts! This book definitely falls within the class of "The old way of teaching ODEs".

That being said, the book wasn't bad, I skipped chapters 8 and 14, and am sure I will come back eventually to finish those too.

[Negar Moradi · Rating 3 out of 5]

If you are a Mathematics student I do NOT recommend it! It is useful for Engineers who are not interested in Mathematical proof.

[Gia-Bao · Rating 5 out of 5]

The special thing about this book is that the author provides the readers with historical notes on the stories of the great mathematicians, how the problems were solved and how the theorems were formulated. In any other book on differential equations one can find solutions and methods of solving differential equations, but only a few - this one belongs to those - can one read with passion and curiosity.

[Nischay Namdev · Rating 5 out of 5]

good book

[Omar · Rating 5 out of 5]

Great introduction to differential equations with emphasis on both theory and practicality. I highly recommend it

[Kent Sibilev · Rating 3 out of 5]

It is a pretty good introductory text on ODE. The historical interludes are a nice bonus. But if you are looking for rigor and more details, look somewhere else.

[HikBook]

A complete book about ODE

[Arunfrangln]

review

[Pratik Bambhania]

good

[Venkata Rama]

fads

[Matías · Rating 4 out of 5]

No lo leí entero, fuí directo a lo que la facultad estaba demandando, pero me encantó.

Esto junto con Khan Academy fueron lo mejor que me pasó en ecuaciones diferenciales.

[Anchal Gupta]

hjm