General texts on systems of partial differential equations?

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Discussion Overview

The discussion revolves around the search for general textbooks on the properties and solutions of systems of partial differential equations (PDEs), particularly focusing on vector and tensor valued PDEs such as Maxwell's equations, Navier-Stokes equations, and equations related to elasticity and deformation of solids. Participants express a desire for resources that integrate these topics within a broader theoretical framework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for modern textbooks that cover the general theory of vector and tensor valued PDEs, emphasizing the need for resources that connect various specialized topics.
  • Another participant suggests a specific book but acknowledges that it may not meet the request for a more contemporary text aimed at graduate and postdoctoral mathematicians.
  • A later reply reiterates the need for a book that does not focus on single, scalar valued PDEs, indicating prior knowledge in that area and a preference for texts that delve into vector valued systems.

Areas of Agreement / Disagreement

Participants generally agree on the need for more modern and comprehensive texts on vector and tensor valued PDEs, but there is no consensus on specific recommendations that meet all criteria outlined by the original poster.

Contextual Notes

Some limitations include the potential focus of suggested texts on scalar valued PDEs rather than the desired vector valued systems, as well as varying levels of assumed prior knowledge among participants.

The Bill
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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.
 
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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.
 
The Bill said:
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.
 
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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.
 

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