Calculus reform: the first semester
Calculus: The current version of the first semester calculus course
(Math 101) I am teaching has two goals:
- 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.
Here are some topics included in this course:
- 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)