My question has already been asked in this site but I want to make an effort and explain what exactly I want from that PDE book, since no book that I looked at(at least from their contents) is satisfying for me.
Well, I took a class in my university which was a combination of ODE and PDE. Because of the great content that we had to cover in one semester, it is obvious that the lessons couldn't have been with more detail. As far as the topics we covered in PDEs, we talked about Sturm-Liouville problems(the simple ones) and we solved PDEs with homogeneous BCs using separation of variables. We made a little reference on how to solve PDEs with non-homogeneous BCs, but we only saw very specific and simple cases(which many books also do).
What I look is a book that completely covers linear PDEs, as long as Sturm-Liouville problems, and not emphasizing on homogeneous cases(either regarding the BCs or the PDE itself), if possible with some mathematical rigor. The reason I want that is that I attend a lesson about physics of vibrations and there are many non-homogeneous PDEs that appear when solving the wave-equation.
Thanks for any recommendations in advance!
P.S.: As you see, my whole concern is about non-homogeneous BCs. If there are any online-sources that are related to this topic, please copy it and paste it as an alternative to bying a whole book.