This year for calculus we will be using Google Classroom.
The general outline for 2nd semester is to begin with applications of derivatives (curve sketching, related rates, and optimization). The general idea here is to see how we can leverage the idea of rates of change/slope/derivative to understand the behavior of non-linear functions.
From there we will step into the Fundamental Theorem of Calculus. We will prove it directly through the formal definition of the limit of a Riemann sum, and use that to flesh out the basic techniques for integration (up to and including base u-subs).
Finally, we will use the concept of the integral of 1/x to expand the set of functions that we can work with, developing a rigorous definition for exponentials and logs, which prove more widely applicable than the introductory methods given in algebra.
Syllabus
The general outline for 2nd semester is to begin with applications of derivatives (curve sketching, related rates, and optimization). The general idea here is to see how we can leverage the idea of rates of change/slope/derivative to understand the behavior of non-linear functions.
From there we will step into the Fundamental Theorem of Calculus. We will prove it directly through the formal definition of the limit of a Riemann sum, and use that to flesh out the basic techniques for integration (up to and including base u-subs).
Finally, we will use the concept of the integral of 1/x to expand the set of functions that we can work with, developing a rigorous definition for exponentials and logs, which prove more widely applicable than the introductory methods given in algebra.
Syllabus