Is Piaggio's Differential Equations worth reading?

[yucheng]

I got to know of this book through Freeman Dyson's obituary. Just wondering, is it useful in studying Physics (it seems to cover everything), do people even use it these days? I understand differential equations are basically half of Physics. By the way, this book is really old, are there any better, newer ones?

 

[S.G. Janssens]

It looks like Piaggio has written a number of books on the topic. Do you mean An elementary treatise on differential equations and their applications with a first edition from 1920? There is some history about that. While I do not know this book myself, I have two comments that may be useful.

Since the first half of the 20th century, the accent in teaching and research on DEs has changed quite a bit, from finding explicit solutions of specific equations towards studying qualitative behavior of families of such equations. This does not mean that the classical perspective is any less useful, but it does mean that a more modern book (maybe something not dating back further than the 1960s recent) may give you a more complete picture. I would choose a book that offers both perspectives and also refers to the older literature.

In general, older books can still be very useful. Sometimes they contain somewhat forgotten but very valuable knowledge. (Some of my favorite analysis books first appeared in the 1950s.) However, for a first encounter, more modern books can be more useful, as long as they contain a good bibliography that does not ignore older and original publications.

Maybe someone else knows more about Piaggio's book proper. If you need other suggestions, I can provide them. What is your background?

 

[yucheng]

@S.G. Janssens, I am self-studying Physics and Mathematics. I still have a very long way to go; just started reading Terence Tao's Analysis. I also got Boas' Mathematical Methods for the Physical Sciences, but it seems to gloss over a lot of theory, and thus makes it hard to understand (plus I enjoy theory too, not just application)...

 

[S.G. Janssens]

I am self-studying Physics and Mathematics.

Nice! Maybe check out micromass's Insight articles at some point.

I still have a very long way to go; just started reading Terence Tao's Analysis.

Good choice.

I also got Boas' Mathematical Methods for the Physical Sciences, but it seems to gloss over a lot of theory, and thus makes it hard to understand (plus I enjoy theory too, not just application)...

"Methods" books do that sometimes. It's a certain style, and from my own experience I can understand your preference for a different style.

I can think more about it, and other will probably chime in as well, but here is already one book that might appeal: Ordinary Differential Equations and Dynamical Systems by Teschl. The author has made it available for free.

The author's research interest is in mathematical physics and DEs. Apart from some notation that I find awkward, I think it is a good book. Given your background knowledge, it may be slightly early to try, but we used it as the supplementary text for second year undergraduate students of DEs. In any case, you can easily have a look.

 

[MidgetDwarf]

@S.G. Janssens, I am self-studying Physics and Mathematics. I still have a very long way to go; just started reading Terence Tao's Analysis. I also got Boas' Mathematical Methods for the Physical Sciences, but it seems to gloss over a lot of theory, and thus makes it hard to understand (plus I enjoy theory too, not just application)...

If it is your first encounter, then maybe look at Ross: Differential Equations. Do not get the book titled Introductory. The Differential Equations books contains the Introduction to Differential Equations, but more topics for a second course. I remember Micromass recommending this book to me. It is very easy to read and work through. Maybe supplement it with a cheap copy of Zill: Differential Equation (cheapest edition you can find) for about $5-$10. You don't necessarily have to read Zill. The explanation in Ross is superior, but Zill has lots of problems... So use Zill more as a workbook.