Lecture 5, September 14 and Lecture 6, September 17
Section 2.1 is NOT on the course outline but contains good
motivational examples.
Section 2.2:
I tried to motivate the concept of limit through ideas about
approximating numbers. We looked at the definitions of ordinary,
one-sided, and infinite limits and vertical asymptote.
Apology: I started an awkward example;
I did not do with it what I had originally planned, and
the material I started in class is beyond the scope of
the course. If you want to see how that should have been
finished, here is some supplementary reading:
Lecture optional example
Lecture 7, September 19 and Lecture 8, September 21.
Section 2.3:
Calculating limits using the limit laws. We studied the laws and
did a range of typical examples. We discussed the important Limit
Comparison Theorem and the even more important Squeeze Theorem.
Section 2.4 is NOT part of the course, but may prove useful
reading for those of you interested in the theory behind limits.
Lecture 9, September 24 and Lecture 10, September 26.
Section 2.5:
Continuity. Definition, examples, and the important Intermediate
Value Theorem (IVT).
Lecture 10, September 26, and Lecture 11, September 28.
Section 2.6: Limits at infinity, horizontal asymptotes.
Definitions and examples.
Lecture 11, September 28, and Lecture 12, October 01.
Section 2.7: Tangent lines, rates of change, and derivative
at a point
Lecture 12, October 01, and Lecture 13, October 03.
The derivative as a function
Lecture 13, October 03.
'Differentiable implies continuous', higher order derivatives.
