Music, April 22, 2013
We review functions in the context of music. The topic allows to see
how functions are built up from basic functions, review the
exponential function, the trig functions.
We learn what it means to change the frequency c and amplitude A in A sin(c x)
or how to implement amplitude or frequency modulation.

Statistics, April 24, 2013
This lecture introduces probability density functions, cumulative distribution functions,
and the expectation. Examples cover the exponential distribution, the normal
distribution and the arcsin distribution. This lecture aims to
review integration techniques like trig substitution and integration by parts.

Economics, April 26, 2013
This lecture reviews what it means to have a maximum or minimum and
derives a theorem in economics which deals with marginal cost f(x), total
cost F(x) and average cost g(x) F(x)/x. This theorem tells that the breakeven point
f(x) = g(x) is an equilibrium point g'(x) = 0. The theorem is illustrated
with strawberries.

Computer Science, April 29, 2013
This lecture deals with integration of functions. We find a way to generate random
functions and then differentiate them to get integration problems. We also discuss
some general difficulties of artificial intelligence like finding patterns or
errors in proofs.

Thanks to the
Harvard Bok Center for teaching and learning
for videotaping these four lectures . The recording was intended to be part of the HILT project
"Calculus practitioner series: Meeting the changing needs of our students and client disciplines" which had the goal:
"Awardees plan to design and record a multimedia series on the interdisciplinary nature of calculus with speakers from
Harvard faculty from the STEM and quantitative social science fields." .
The project was funded by a
Hauser grant .

