Calculus I
Official Description[edit]
Calculus I (17-120)
An introduction to single-variable calculus. Topics include intuitive treatment of limits and continuity, differentiation of elementary functions, curve sketching, extreme values, areas, rates of change, definite integrals, and the Fundamental Theorem of Calculus.
Overview[edit]
Limits, differentiation, and integration.
What actually happens[edit]
In Calc I, you start by examining functions, and making sure you can draw the basic ones. Then you get into limits (as x approaches c, f(x) approaches L), and continuity. One chapter later, you're doing derivatives using the limit definition, but then you learn the power, product, and chain rules, and you're set. Then you spend a chapter with applications of differentiation (taking derivatives), simple differentials (another way of writing derivatives), and implicit differentiation (fun new ways of looking at the chain rule). At this point you will have taken care of everything in the course description except areas, definite integrals, and the Fundamental Theorem of Calculus. In chapter four, you approximate area using Riemann sums, which leads you nicely into Riemann integrals (Riemann sums in which the interval approaches zero). The Fundamental Theorem of Calculus is one of the last things you learn, and it simply states that the definite integral from a to b is equal to the difference between an indefinite integral evaluated at b and the same indefinite integral evaluated at a. (Math isn't rendering.)
