Introduction to Calculus and Study Guides

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!

My sections of Calculus primarily cover the Advanced Placement (AP) AB course. I have to admit that I was never really “got” calculus in high school. 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!

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). Even before learning Differentiation, calculus address Limits, since we need limits (the concept of things getting closer and closer without actually touching) to “understand” the foundation of Differential Calculus.

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 Differential Calculus!