Video Lecture

Recording Information:
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 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.

Section Information:
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.

Lecture Description: On this day of lecture we started to discuss the method of substitution (change of variables) for computing indefinite integrals. The textbook which accompanies 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:

  • 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.

Condensed Lecture Video:

Full Length Lecture Video: