Another good QM book for those with a linear algebra background is A Modern Approach to Quantum Mechanics by Townsend.
In my undergrad physics program we were required to take a PDE class taught by the physics dept. The text we used was Partial Differential Equations with Fourier Series and Boundary Value Problems by Nakhle H. Asmar. It has been a good reference book and the second half of the book focuses on applications of PDEs. For example, there is a section on elastic vibrations and buckling of beams, and there is an entire chapter discussing the PDEs used in quantum mechanics.
