Calculus reform: the first semester

• To teach the old-fashioned formula-driven calculus, in particular, teaching that the notation tells us what to do.

• To teach calculus as an introduction to mathematical thought, much as an introductory course in the other sciences can be an introduction to the subject as a whole.

• The standard geometric Brownian motion model of stock prices as a generalization of exponential growth/decay.

• Simple differential equations, followed by more advanced ones like the SIR model (for infectious diseases) and predator-prey, including computer simulations of the solutions. (The premise of the five-college text Calculus in Context is that differential equations are the fundamental objects in calculus.)

• Newton's method for solving equations, followed by fractals generated in the complex case.

• Material from the 1748 calculus book by Maria Agnesi, which is in our rare book collection. (Agnesi)

• Carbon-14 dating using some interesting examples (Carbon-14)