Vaughn Climenhaga

Associate Professor
Department of Mathematics
University of Houston

Math 2413

Calculus I -- invitation-only section, 14862
Fall 2021

If you have received an invitation to this section and would like more information about it, please see the material below, or email me.

Instructor: Vaughn Climenhaga
  • Email: climenha [at]

TA: Jason Day (jjday [at]

Course information:
  • Lectures:  MWF 9-9:50am, S 119
  • Labs:  MWF 10-10:50am, S 119
  • Textbook:  James Stewart, "Calculus: Early Transcendentals", 8th edition
  • Supplementary text:  Michael Spivak, "Calculus"
In this course we will study differential and integral calculus, including continuity, limits, derivatives, optimization, intermediate and extreme value theorems, Riemann sums, integration, the fundamental theorem of calculus, areas, and volumes.  A strong emphasis will be placed on conceptual and intuitive understanding, on clear and precise definitions and theoretical notions, and on the central role that calculus plays in the scientific world.

If you received an invitation to join this class, you might be wondering whether you should enroll in this section or in the main calculus course. If you received an invitation and already have AP calculus credit that would let you proceed directly to a later calculus course, you may be wondering whether it is worth taking this course and revisiting material you have already seen. I hope the following information is useful as you make your decision.

FAQ about the invitation-only section

As the FAQ document indicates, this section includes a deeper theoretical treatment and a broader view of applications compared to the main sections. To get a better feel of what that means, the following two videos illustrate the kind of discussion that will occur in this course, but probably not in the main sections or in an AP class. (You may need to sign in using your UH account to view the videos; please email me if you have trouble.)

Defining the sine function (40 minute video, theory) -- notes
Calculus and rainbows (43 minute video, application) -- notes

The majority of the course will consist of the same topics as those that appear in the main sections, but I hope that those videos give you some sense of how this section goes beyond what you would find there. When I began my own undergraduate studies, I had already taken calculus in high school and had the option of using that credit to skip over the first semester of calculus; nevertheless, I was persuaded to enroll in a special section that covered the material I had already seen, but from a deeper and more advanced point of view. That proved to be one of the formative experiences of my mathematical career and serves as some of the inspiration for my own teaching in this course. If you have been invited to enroll in this section, and if it appears to be a good fit based on the information above, then I hope that you will join me on the journey this semester.

Finally, if you want to really see what we did the last time I taught this course, you can have a look at my typed lecture notes for Calculus 1 and Calculus 2. Note that those are somewhat rough and unpolished, and certainly contain errors, which I will hopefully find and correct as I produce a more refined version this year.

Homework assignments
See course page on BlackBoard
for HW assignments and solutions