Textbook for learning PDE's applied to physics?

[Vannay]

Took a graduate level mathematical methods for physics course and came out the other side feeling a bit lacking in solving stuff like the heat equation, wave equation, laplaces equation and so on. I'm still unsure of the Green's Function method for them, how to look at them with Fourier series, and so on.

The textbook we used was Goldbart and Stone which often would introduce the Green Function method for a given PDE by saying "So here's the solution" and then showing it is. That doesn't help when I'm taking a test that says solve this diffusion PDE given these certain boundary conditions.

 

[Dr Transport]

Haberman or Pinsky...

https://www.amazon.com/dp/0321797051/?tag=pfamazon01-20

https://www.amazon.com/dp/0821868896/?tag=pfamazon01-20

 

[UnivMathProdigy]

I really like the books from Lokenath Debnath (they're kind of expensive, though):

(Linear PDEs) https://www.amazon.com/dp/0817643931/?tag=pfamazon01-20

(Nonlinear PDEs) https://www.amazon.com/dp/0817682643/?tag=pfamazon01-20

 

[deskswirl]

Never trust a book on Green's functions whose cover isn't green....

That being said Duffy's book:
https://www.amazon.com/dp/1482251027/?tag=pfamazon01-20