Analysis General texts on systems of partial differential equations?

[The Bill]

What are some good general textbooks on the properties and solution of systems of partial differential equations? I'm most interested in the general theory of vector and tensor valued PDEs like Maxwell's, Navier-Stokes, and the bulk equations governing elasticity and deformation of solids, etc.

I'd like to read some books that handle all these in the framework of a general theory to help tie together what one learns from specialist books on E&M, fluid dynamics, etc.

 

[NumericalFEA]

https://www.amazon.com/dp/0486664228/?tag=pfamazon01-20

 

[The Bill]

That looks like an interesting book, but I'm looking for a more modern text, written for an audience of today's graduate and post doctoral mathematicians.

 

[theBin]

That looks like an interesting book, but I'm looking for a more modern text, written for an audience of today's graduate and post doctoral mathematicians.

By Richard Haberman, in 2012: "Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5/e". Prerequisites: multivariable calculus, linear algebra I, complex variable !, first course in ODEs for the sciences. For one of the 22 math courses offered at distance learning by Athabasca University (Alberta), the first( and still sole) public Canadian university to be recognized by the Government of USA.

 

[The Bill]

Both of those look like they spend a lot of pages on single, scalar valued PDEs like the heat equation and the scalar wave equation. I've already learned a lot about those. I want a book that assumes you've already taken a course or two dealing with heat equations, Laplace's equation, etc, and dives right into vector valued systems of PDEs.