Calculus is the study of functions and really has three major components:
Limits are the building blocks for Calculus. Almost everything at the beginning is a limit procedure: the idea of gettting "closer" to the actual value by approximation. Determining what these approximations approach is the nature of a limit. Derivatives are approximations of the slope of a tangent line at a point by calculating the slopes of secant lines that move closer and closer to one specific point, a limit process. Integrals represent the area between a function and the \(x\)-axis. By breaking that area down into smaller and smaller rectangle areas, this provides and approximation to the exact area. Each time more rectangles are used, the approximation gets closer to the actual area, a limit process. Understanding limits becomes the most fundamental idea for the rest of the content.
Select a topic within a unit:
Research is showing that students are having difficulty reading in mathematics. One of the goals for this approach is to help students read math. By reading and processing math information on your own, have me fill in the gaps when needed and practicing new problems, I believe you will be successful in this Calculus course.