I am currently a junior in high school, and am at the beginning of my second semester of AP calculus (beginning of the bc portion). While I am able to scrape by with As in the class, I have trouble really understanding the class. It is taught in a very "memorize this formula, do that process, and don't ask questions" kind of way, and I am hopeless at simply memorizing formulas and processes in that way, such that I work more slowly and make more small mistakes than others.
From what I've heard when asking how to remedy this problem, I need to understand in a more "conceptual" way, so that I can figure out the solutions of my own accord rather than just memorizing stuff. Essentially, my question is, is there a more conceptual way of understanding calculus?
I've been able to do exceptionally well in a physics class in this way, mainly because the math there is far more applied to real situations, and I'm great with that kind of intuition. I was able to ignore much of what the teacher said beyond the basics, and was able to find my own way to reach the solution without being methodical in that way. My problem is that I don't know how to apply that intuition to calculus, which is a huge handicap for me as I desperately want to go into astrophysics as a career, which obviously utilizes calculus almost exclusively. I desperately want to have the sort of edge in calculus that I had in physics, especially because you really have to be the best of the best if you want to go into a scientific career.
I've tried working with some friends who are better at the class than I, but almost all of them simply reiterate the same methods in processes that the teacher has taught, without explaining why or how to draw that conclusion on an intuitive level. Most websites that I've found either do the same thing or give only hints of the concepts themselves. In particular, I've attempted to make small excursions into Paul's Notes, but ultimately end up getting bogged down in the trivialties and have to spend as much time understanding the math there as I do in a lecture. In addition, other sites start with beginning concepts that I have long since learned, forcing me to sort out the things I already was taught. I'm further wondering, where exactly can I go or what can I do to get a better, more conceptual understanding of calculus?
I've been spending a lot of time lately trying to figure out how to accomplish this understanding, and given my aforementioned experience in physics, I think I have the ability to do so. I don't know if I'm thinking through this all wrong or if calculus really is a completely new form of math that I simply won't be able to grasp. At the rate I'm going, I'm beginning to question my ability to get a respectable grade on the AP exam, and I'm willing to put a lot of work into becoming better, if possible.