Thermodynamics and heavy use of partial derivatives

Hello,

I am not completely certain why in thermodynamics, it seems that everything is done as a partial derivative, and I am wondering why? My guess is because it seems like variables are always being held constant when taking derivatives of certain things, but it is still somewhat a mystery to me.

Also, I noticed since starting my chemical engineering class, a lot of things are approximated, it seems like there aren't a lot of closed form solutions to thermodynamic problems and numerical methods must be used.