The video below was filmed on November 27th, 2017 at the University of
Pittsburgh and is a recording of my Calculus I (MATH220) lecture. Please visit
http://calculus.math.pitt.edu for the course syllabus
and a list of topics covered.
The total length of the lecture is 48 minutes and I have
provided both a full-length video as well as a
condensed version for easy viewing.
There are 75 students enrolled in my section of Calculus I.
Most students are majoring in Engineering, Biology, Chemistry,
or Computer Science.
There are very few Mathematics majors/minors in this class.
Attendance on the day of the recording was approximately 63.
On this day of lecture we started to
discuss the method of substitution (change of
variables) for computing indefinite integrals. The textbook
this lecture is Essential Calculus: Early Transcendentals,
second edition, by James Stewart. In the previous lecture, the students
learned the Fundamental Theorem of Calculus and how it can be
used in evaluating definite integrals.
Structure of this Lecture:
Condensed Lecture Video:
Five minutes before each class begins, I put a set
of warm-up problems on the board which are
based on the material covered during the previous lecture
(in this particular class,
using the Fundamental Theorem of Calculus to
evaluate definite integrals).
Students begin working on them individually as soon as they arrive
to the classroom and then share their work in pairs for the
first couple minutes of class.
(This section is omitted from the recording.)
- After students worked in pairs I solved
each warm-up problem and then used this discussion
to set the stage for the topic to be covered that day.
There are very few proofs presented in this class; however,
I provide at least an intuitive idea behind the mathematics
they are learning whenever appropriate.
- The remainder of this lecture focused on solving
problems with varying degrees of difficultly. At every stage,
I include my students in the discussion by using their
ideas to solve the problem.
- I end each class by adding a few problems to the lecture
notes (available online for students to view after class)
for students to work on before the next lecture.
Full Length Lecture Video: