When arrived at my school a lot of (CS,PMATH) professors told me that they didn't believe that Calculus should be anyone's introduction to mathematics. Unfortunately, a lot of Calculus tends to be taught with "tricks" (this includes a fair number of proofs) that while are neat to look at as a math major provide very little benefit to most people.

One of the best things that happened to me was our first year classical algebra. It starts from the very basics of logic, surveys elementary number theory, modular arithmatic, complex numbers and puts a very large emphasis on constructive proofs. It was a course where you actually began to understand mathematics rather than just use it. I think I realized I was studying the right subject when I spent about six hours in our tutorial centre proving some arbitrary property about GCDs with about ten other people. Anyway, after I had finally solved it, I rode my bike home, collapsed in my bed out of mental exhaustion. Of course, when I awoke I realized how much I had learned in the process of the proof.

After learning logic and the basis of proofs, Calculus begins to make *a little* more sense. A lot of people get scared the first time they see something like the precise definition of a limit; but a strong logical background makes it quite seemless.

Anyway - it might be worthwhile to see if the school has a first year "proofy" class that you can get yourself into. Otherwise, it might be worthwhile to read a book on basic mathematical logic or number theory. Even if you can't recreate proofs, there is a lot of benefit in reading them. Of course, if it is just manipulating equations that you need help with I'm sure it will come in time.

(That course is Math 135/145 for anyone at Waterloo)