>>11751180I had a class where I have to do analysis and
solve various PDEs. I felt real dumb with this,
so you're not alone. The midterm test was a
complete massacre, despite open notes.
To help deal with it a little, some of the
ideas in ODEs translate into PDEs, like chain
rule or integration by parts--it's a generalization
of something that you can take advantage of.
The rest are unique to PDEs and needs careful
reading to bring separate derivatives of separate
dimensions with a bunch of pluses in between
into perspective.
If you'd like, the book I used in class was:
"A Course on Partial Differential Equations"
by Walter Craig. You can use any other source
as you need.