This website is to keep me (Oliver) organized and in order not to
have to email around too much and have all links on one page and also
in order to have a backup refereal in case of technology failure.
You can reach me always by email knill@math.harvard.edu. This semester
I have by default open office doors Tuesday/Thurday 9-10 AM. You should know
the zoom link, otherwise email.
Announcements
Week 13 features
the method of substitution and a final wrap-up lecture.
Exam 3 takes place December 10 to December 12.
Week 12 features
the fundamental theorem of calculus after reviewing some
properties of the Riemann integral. Included in this folder
is also the Monday, November 23 lecture before thanksgiving.
Week 11 wraps up limits
and deals then mostly with integration.
Week 10 deals with
Hopital's rule and comparing rates. This is also an exam week.
Week 9 covers more related rates,
and how to compute the derivatives of inverse trig functions.
The last lecture of Friday reviews some related rates and extrema
problems.
Week 8: does more extremization (now also
using all differentiation rules), then
implicit differentiation and finally logarithmic differentiation.
Week 7: is dedicated to differentiation
rules. The product rule, the reciprocal rule and the quotient rule.
The second lecture features the chain rule.
Week 6: is dedicated to extremization.
Critical points f'(x)=0 are candidates for maxima and minima. We also
look at the Bolzano extremal value theorem for continuous functions
on an interval and then some applications.
Week 5: we first look at linearity and
the power rule and how to plot functions by using the signs of f,f' and f''
the second lecture features linearization and the exponential function.
The third lecture initiates the second project. Exam week!
Week 4:
In this fourth week, we look more about how to compute limits,
compute limits for x going to infinity and then review again the
relations between functions, its derivative and its second derivative.
Week 3:
The themes are limits and continuity. There are three lectures
We first look at the derivative as a function, then look closer
at limits and then define continuity and see how it can fail.
Week 2:
The theme is rate of change. There are two lectures:
in the Wednesday 9/9 lecture, we look at average rate of change
and instantaneous rate of change graphically as the slope of
tangent lines. On the Friday 9/11 lecture, the definition and
the interpretation of the derivative appear.
Week 1:
The theme is modeling with functions. There are two lectures.
In the Wednesday 9/2 lecture, we get to know each other, and start to
look at a problem.
In the Friday 9/4 lecture, we do more modeling.