Old, but EXTREMELY useful explanation of techniques for (exactly) solving PDE's (coordinate transformations for separation, complex variable analysis for understanding of critical points, eigenvalue analysis of resulting ODE's, Green's function and integral equation techniques).

The classic text for applied mathematics. This is truly a work of art - with its clear explanations and its fantastic stereoscopic illustrations. Yes, it may be a little dated; and yes, it is definitely not an easy read; but its clarity of content and its sheer mathematical elegance make it more than worthwhile for any serious student of physics or engineering. And one thing is certain: anybody able to successfully complete and really understand the material presented in this book will have become very well versed in applied mathematics. - From a review on Goodreads