I have to admit; I was one of those in high school and even college who never really “got” calculus. I could go through the motions of doing really hard problems, but some of the time, never really understood why I was doing them, at least for the more difficult concepts.
Calculus can be that way; and sometimes it’s all right! I hope to be able to help you know what you need to understand and what you just need to be able to do, when going through your Calculus classes. Honestly, there are some parts that I still don’t really understand; there are some really difficult concepts, and I was never the best with Physics!
This first section of Calculus will cover the Advanced Placement (AP) AB course, since that’s what I typically tutor. I hope to eventually cover the more advanced BC course, and I will indicate it as so.
To simplify, typically your first calculus class has to do with rates of things (Differentiation) and area of things (Integration). What calculus adds to what you’ve been doing in Algebra and Geometry is that the concepts are extended to finding rates and areas of curvy things (lines and 3-D objects); it was first invented in the 1700’s (possibly earlier!) to be used in many concepts in Physics (not my favorite subject!) J
In fact, calculus grew from some problems that European mathematicians were working on during the seventeenth century: general slope, or tangent line problems, velocity and acceleration problems, minimum and maximum problems, and area problems. Now, Calculus is used every day in such fields as engineering, physics, computer science, astronomy, epidemiology, chemistry, medicine, statistics, economics, music, meteorology, and more!
Calculus usually starts out with the study of limits, which can be quite frightening and confusing. This is because we need limits to “understand” the foundation of Differential Calculus, since we need to see what happens when graphs get closer and closer together to something until they are basically touching. Also, we need to “appreciate” the math before we plug away at doing it much easier.
Here are links to the Quick Study Guides I created for Calculus:
There is also an excellent review sheet for AB Calculus here.
It’s always good to have a good Algebra review before studying Calculus, too: Algebra Review.
On to Limits and Continuity!