Which Books Offer a Geometric Understanding of PDEs?

[ank_gl]

Hi

I am looking for a good book on PDEs. By good, I mean geometrically intuitive. Something like H M Schey's book on vector calculus.

I know a bit about solving PDEs, I know they are elliptic, hyperbolic or parabolic, characteristic equation defines the type & that's just about it. What I am trying to understand is, what is PDE when it is elliptic or hyperbolic or parabolic. How does it behave geometrically. For example, for a hyperbolic equation, characteristic equation defines a curve or a surface or something across which functions do not relate.

Right now, I have this book. I heard text by Arnold Vladamir & I G Petrovsky are good. Reviews?

Thanks
Ankit

 

[ank_gl]

No body is doing PDEs? :(

 

[pasmith]

Hi

I am looking for a good book on PDEs. By good, I mean geometrically intuitive. Something like H M Schey's book on vector calculus.

I know a bit about solving PDEs, I know they are elliptic, hyperbolic or parabolic, characteristic equation defines the type & that's just about it. What I am trying to understand is, what is PDE when it is elliptic or hyperbolic or parabolic. How does it behave geometrically. For example, for a hyperbolic equation, characteristic equation defines a curve or a surface or something across which functions do not relate.

I heard text by Arnold Vladamir & I G Petrovsky are good. Reviews?

I'm not familiar with those, but I can recommend Applied Partial Differential Equations by Ockendon et al (Oxford University Press, revised edition 2003). It's not in the same style as Schey but its focus is on understanding PDEs which arise in practical applications rather than on abstract rigourous analysis.

I can also suggest Analytic Methods for Partial Differential Equations by Evans et al (Springer Undergraduate Mathematics Series, 1999).

 

[Astronuc]

No body is doing PDEs? :(

If one had bothered to look around PF, one would have found the Math & Science Learning Materials section in which one would find Calculus & Beyond Learning Materials in which one would find a thread:
Partial Differential Equations

There are many online resources of course lectures/notes on the subject, and in some cases, on-line textbooks.

 

[rezeew]

Hi Ankit,

It sounds like you have a good understanding of the basics of PDEs, such as their types and how to solve them. To gain a more geometric understanding of PDEs, I would recommend looking into books that focus on the applications of PDEs in specific fields, such as physics or engineering. These books often provide real-world examples and visualizations of how PDEs behave in different situations.

In terms of specific book recommendations, I am not familiar with H M Schey's book on vector calculus, but I have heard good things about Arnold Vladamir's book "Ordinary Differential Equations" and I G Petrovsky's book "Partial Differential Equations" as well. I would suggest reading reviews and checking out sample chapters to see which one resonates with your learning style the most. You could also try reaching out to other scientists or mathematicians in your field for their recommendations.

I hope this helps and good luck with your studies!

Best,