Calculus Textbook for learning PDE's applied to physics?

AI Thread Summary
The discussion centers on challenges faced in a graduate-level mathematical methods for physics course, particularly in solving partial differential equations (PDEs) like the heat, wave, and Laplace equations. The Green's Function method and its application, especially in relation to Fourier series, are highlighted as areas of confusion. The course's textbook, Goldbart and Stone, is criticized for not providing sufficient problem-solving guidance, leaving students unprepared for practical applications in exams. Recommendations for alternative resources include works by Haberman, Pinsky, and Lokenath Debnath, though the latter is noted to be expensive. Duffy's book is also mentioned as a potential resource for better understanding Green's functions. The discussion emphasizes the need for textbooks that offer clear problem-solving strategies rather than just solutions.
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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.
 
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