I have a mac book pro. the hard drive has been partitioned so that i can run both mac and pc applications. can i use time machine to back up my entire computer - including the pc side?
In a word no.
Time machine will only back up the macOS part of the computer.
There are utilities built into macOS that will allow you to capture an entire disk but require the use of the Terminal (like dd). There are also third party utilities (example: winclone) that will back up the Windows partition while in macOS.
If you don't mind booting into Windows it has an automatic backup utility that will work over a network mounted drive.
But Time Machine just won't do it, you will have to seek other backup avenues.