What topics in Calculus IV are typically in a PDE course?

[Eclair_de_XII]

Additionally, what topics from that same course are relevant to probability? I ask because I'm afraid I might forget some of the topics from my calculus series after one semester of disuse. I mean, I know I should probably brush up on my calculus skills in preparation for any math class that uses it, but it would be nice to have a good idea of what in particular I should study for these courses:

Partial Differential Equations I
Integral surfaces and characteristics of first and second order partial differential equations. Applications to the equations of mathematical physics. Pre: Calculus III, or consent. Recommended: Calculus IV and Intro to ODEs.

Probability
Probability spaces, random variables, distributions, expectations, moment-generating and characteristic functions, limit theorems. Continuous probability emphasized. Pre: Calculus IV (or concurrent).

Any insight on what calculus topics that are relevant to these classes will be much appreciated.

 

[jambaugh]

My first PDE's course focused on BVP for the Heat equation via Fourier series expansion of solutions... the base math for this would be, partial derivatives (of course), some linear algebra concepts, integration methods as needed to carry out integral transforms including some multiple integration. Also some of the series analysis from Calc II is important.

[EDIT] PS. You can search for syllabi for the courses you're interested in and see what topics are listed, and als check textbooks TOC's online.