Resources for general vector differential equations?

[The Bill]

I'd like a good set of notes or a textbook recommendation on how to approach vector differential equations. I'm looking for something that isn't specific to one type of application like E&M, fluid dynamics, etc., but draws heavily from those and other fields for examples.

I'd strongly prefer a conversational, intuition-heavy book that doesn't leave huge gaps "as an exercise" in critical proofs.

I'd also prefer a text that uses differential forms where appropriate, but that's less important as long as the treatment of the subject matter is handled well in general.

 

[Frabjous]

Are you talking about partial differential equations?
There is always the classic work of an olde timey physicist
Partial Differential Equations by Sommerfeld

 

[vanhees71]

Yes, Sommerfeld, Lectures on Theoretical Physics, vol. 6 (Partial Differential equations), is a masterpiece. A bit more modern is the textbook by @Orodruin , containing a lot of the mathematics (particularly vector calculus) you need as a prerequisite to understand the partial differential equations of physics (potential theory aka. elliptic, heat/diffusion equations, aka parabolic, and wave equations, aka hyperbolic PDEs):

M. Blennow, Mathematical Methods for Physics and Engineering, CRC Press (2018)

 

[Orodruin]

A bit more modern is the textbook by @Orodruin , containing a lot of the mathematics (particularly vector calculus) you need as a prerequisite to understand the partial differential equations of physics (potential theory aka. elliptic, heat/diffusion equations, aka parabolic, and wave equations, aka hyperbolic PDEs):

M. Blennow, Mathematical Methods for Physics and Engineering, CRC Press (2018)

I generally don't like to bang my own drum, but I won't argue with this either.

 

[The Bill]

Are you talking about partial differential equations?
There is always the classic work of an olde timey physicist
Partial Differential Equations by Sommerfeld

What I'm asking about is more specific. Vector valued partial differential equations. Ideally, a textbook fitting this thread would assume the reader had already completed a course on scalar valued partial differential equations and had some familiarity with specific systems of vector valued partial differential equations like Maxwell's equations and the Navier-Stokes equations.

What I'm looking for is material that builds general tools and intuition for tackling systems of vector valued PDEs in general, from the beginning. That would be the entire focus of the text I'm looking for.

 

[Bae3uyei]

I'd like a good set of notes or a textbook recommendation on how to approach vector differential equations. I'm looking for something that isn't specific to one type of application like E&M, fluid dynamics, etc., but draws heavily from those and other fields for examples. I thought to find it on https://plainmath.net/secondary/algebra/algebra-i/polynomial-graphs where there are always answers to any problems and questions with free solutions to polynomial graphs problems and not only. But in any case, I'm interested in the supplement resources.

I'd strongly prefer a conversational, intuition-heavy book that doesn't leave huge gaps "as an exercise" in critical proofs.

I'd also prefer a text that uses differential forms where appropriate, but that's less important as long as the treatment of the subject matter is handled well in general.

Have you tried looking for something similar in local scientific libraries? Very often we underestimate these places in the 21st century

 

[The Bill]

Have you tried looking for something similar in local scientific libraries? Very often we underestimate these places in the 21st century

If I get a recommendation that is a textbook, I'll certainly check my local university library, and get it through interlibrary loan if they don't have it.