As the title, are there any good reference texts for introduction to partial differential equation?
I think the answer to your question depends on whether you’re more interested in the theory of partial differential equations or in how to compute the solutions to concrete equations.
At a more theoretical level you can try Ronald Evans’ Partial Differential Equations: Second Edition (Graduate Studies in Mathematics). This is one of the most complete textbooks on PDEs around, I think.
On the more practical side, you can try Polyanin’s Handbook of Partial Differential Equations. This is more of a solution recipe book, but has interesting tips and ideas on how to tackle a large number of problems.
I would recommend “Partial Differential Equations with Fourier Series and Boundary Value Problems” written by Asmar. It is a text for beginners in the subject, but eventually it gets very far, to a thorough treatment of Green’s functions. It does also include a lot of material on Bessels functions.