Which Books Offer a Geometric Understanding of PDEs?

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Discussion Overview

The discussion centers around the search for books that provide a geometric understanding of partial differential equations (PDEs). Participants express interest in resources that explain the behavior of PDEs in terms of their geometric properties, particularly in relation to their classification as elliptic, hyperbolic, or parabolic.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Ankit seeks recommendations for books on PDEs that are geometrically intuitive, similar to H M Schey's work on vector calculus.
  • Ankit expresses a desire to understand the geometric behavior of PDEs classified as elliptic, hyperbolic, or parabolic, particularly in relation to their characteristic equations.
  • One participant suggests "Applied Partial Differential Equations" by Ockendon et al. as a resource focused on practical applications of PDEs, though it may not align with the geometric style Ankit is looking for.
  • Another recommendation is "Analytic Methods for Partial Differential Equations" by Evans et al., which is also noted but lacks a direct connection to geometric intuition.
  • There is a mention of existing online resources and a specific section on Physics Forums that contains materials related to PDEs.

Areas of Agreement / Disagreement

Participants have not reached a consensus on specific book recommendations that meet the criteria of being geometrically intuitive. Multiple viewpoints and suggestions are presented without agreement on a single resource.

Contextual Notes

Some participants may have different interpretations of what constitutes a geometrically intuitive approach to PDEs, and the recommendations vary in their focus on practical applications versus abstract analysis.

Who May Find This Useful

This discussion may be useful for students or professionals seeking resources that bridge the gap between geometric intuition and the study of partial differential equations.

ank_gl
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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
 
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No body is doing PDEs? :(
 
ank_gl said:
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).
 
ank_gl said:
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.
 

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