Multivariable calculus: hard problems with solutions
Solution 1:
Usually Schaum's outlines are a good source for lots of problems with solutions, in this case
- Elliott Mendelson: Schaum's 3,000 Solved Problems in Calculus
and
- Robert Wrede and Murray Spiegel: Schaum's Outline of Advanced Calculus
come to mind. I don't know if that's hard enough, however :-)