Conceptual Understanding of AP Calculus Ideas
We will go over each of the AP Calculus topics, with a focus on the concepts rather than formulae and exercises (although exercises are necessary for rigorous understanding, they will not be the focus). We will start with the meaning of infinity and a conceptual understanding of limits, and then go on to geometric approaches to differentiation and integration. We will end with sequences and series. I will try to go over differential equations if I get enough time.
You should be familiar with basic algebra concepts (including knowledge of functions), various functions (algebraic, trigonometric, exponential), and algebraic manipulation of equations. It is also necessary to have a willingness for abstract thinking, as calculus requires much of it. This series will especially require abstract thinking, which can be developed throughout the series, but cannot be developed without a desire to understand anything fully.
The series will have some structure, but each session will not have a set topic. It will mainly be a continuation of our discussions in the previous sessions, so I may have to adjust the session topics/descriptions or add more sessions.
Participation is strongly encouraged from anyone joining the series, as the success of this series highly depends on participation. Feel free to unmute and ask any questions you may have at any time - I will be happy to answer!