Sunday, May 21, 2017
preCalculus 2016-2017: 8 Week Calculus Crash Course (May)
8 Week Calculus Crash Course
Calculus Units 2,3 & 5!
As you can see above, my Calculus Crash Course starts with CH03 Rational Functions (2 weeks) about Limits. This is actually the last chapter we cover in the preCalculus text. I add the concept of Limits at a Point and Limits at Infinity when graphing Rational Functions. When we talk about horizontal, slant and non-linear asymptotes, we are really talking about Limits at Infinity. When we talk about vertical asymptotes and holes in the graph, we are really talking about Limits at a Point.
UNIT02 (2 weeks) is from my Calculus class. Here we extend the idea of Limits at a Point to finding the limiting slope of a secant line as it approaches a tangent line. Then we introduce limits involving the Difference Quotient! We also talk about continuity and differentiability.
UNIT03 (2 weeks) is all about developing and applying the algebraic rules for derivatives: Power Rule, Trig Rules, Product Rule, Quotient Rule and Chain Rule. If we have time, we even touch on part of UNIT04 about Implicit Differentiation and Related Rates!
UNIT05 (2 weeks) is about AntiDerivitives. We first work with AntiDerivatives analytically. Then we play around with Definite Integrals and Reimann Sum estimates. We even write a program for LSUM, RSUM and TRAP when calculating areas with large numbers of rectangles! If we have time, we touch on UNIT06 and Volumes of Revolution!
I don't do UNIT01 as it's preCalculus review! We don't really do justice to UNIT04 (applications of derivatives) nor do we have a lot of time for UNIT06 (applications of antiderivatives). Hopefully, my students will take a full semester of Calculus in college next year or a full year in High School and get a lot more practice with these concepts. However, my 8 week crash course is a good introduction to the concepts of Calculus! We barely scratch the surface, but my students could probably pass the AP Calculus AB exam if it were given in June!