I've been studying up in preparation for commencing my astronomy studies at JCU. I'm please to say that I've finally (finally!) found a book that's teaching me partial differential equations. I have nothing but praise for Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.
Some of you may remember me struggling with this in the past. The book I had was rigorous, but lacked examples and practical help. Farlow provides all of this. The book is broken into 47 lessons that take about an hour to complete each. It's not the most exhaustive coverage, nor the most rigorous, but it has provided me with the visceral understanding that is needed to actually go out and solve problems.
I've been thumbing through that older, higher level, text now, and I must say that it makes much more sense.