Many years ago I taught a mathematical class (with calculus) on Intermediate Microeconomics. It covered consumer theory, producer theory and partial equilibrium. I wrote up some notes; they are more mathematical than your traditional Intermediate Micro class.
Here are the lecture notes. Unfortunately these do not include the welfare theorems - I evidently ran out of time.
Here are the homework problems and exams. I've included the solutions. There may be some repetition in here.