Assistant Professor of Mathematics Tulsa Community College

About Analytic Geometry & Calculus 3

Vision for this course

Multivariable calculus is an extension of differential and integral calculus to n-dimensions. It reinforces the students' visualization skills and requires the student to think about how we interpret derivatives, integrals, and vector objects geometrically and in applications. The quizzes and notes below reflect that emphasis in our course. In class, I strive to show the students where each of the formulas come from, what they mean geometrically and in applications, and how to use the formulas and techniques, geometrically and in applications.

I view this course as less about the skill-building that is necessary in Calculus I and II. By the time a student has reached Calculus III, hopefully they understand single-variable limits, derivatives, antiderivatives, and integrals, and how they are interpreted geometrically and in applications. In Calculus III, we extend that understanding to n-dimensions. At this point, some students are comfortable with geometry but not computation, while others are comfortable computing but not comfortable with geometry. In this course, students are stretched to develop (1) their geometric intuition, (2) conceptual understanding, and (3) computational and procedural fluency. We focus on extension and application rather than skill-building here.

The quizzes aren't as straight-forward as they were in Calculus II, because in this course, many concepts, applications, and computations may comprise a single standard. A standard covering vector fields is necessarily more involved than a single standard devoted to integration by parts or volume using cylindrical shells. There are more ideas to connect. The computations themselves aren't difficult if the student is armed with excellent prerequisite skills, but keeping track of notation and the meaning of each mathematical object can be challenging. My goal is to help students meet that challenge. In chapter 16, we'll be able to compute quantities with calculus that would have been unimaginable back in algebra class, if we've done the work of understanding the foundation. It's like going hiking...We're working our way toward a beautiful view.

With these goals in mind, I allow one 8.5" by 11" hand-written, student-created formula sheet for vector identities, graphs of known functions, derivative and antiderivative rules for each quiz. Given our goals, this seems appropriate. (I allow two pages of notes for each unit exam in the online section of this course.) I use standards based grading in the face-to-face sections, and unit exams in the online sections. Lectures focus on derivations, computation, and meaning.

I hope you find multivariable calculus as beautiful as I do.

Analytic Geometry & Calculus 3 (YouTube playlist)

In Spring 2020, I made videos for Calc III. They break the lesson up into small chunks. Some videos are long, because I'm showing you both the concepts and examples of how to solve related problems.

While I don't expect you to watch every video from beginning to end, these resources are here to help you prepare. The videos help you solve the problems that I tend to put on quizzes and exams. I review the details. My students tend to need that review.

Unit 1 - Geometry of Space - Class Notes

Blank class notes and homework are shown below. Students are encouraged to use the class notes to organize their thinking and their study of the material we covered in class. Completed class notes are provided so that students can check their work. This is on the honor system; the expectation is that students will do their own work for learning's sake and use the solutions to check their reasoning. Listed problems are selected from Thomas' Calculus Early Transcendentals, 13th edition.

U1 L1 Vectors and Vector Operations (with Assigned Problems) (12.1 and 12.2) (pdf)Download

U1 L2 Dot Product and Cross Product (with Assigned Problems) (12.3 and 12.4) (pdf)Download

U1 L3 Lines, Planes, and Distance (with Assigned Problems) (12.5) (pdf)Download

U1 L4 Cylinders and Quadric Surfaces (with Assigned Problems) (12.6) (pdf)Download

U1 L1 Completed Class Notes (12.1 and 12.2) (pdf)Download

U1 L2 Completed Class Notes (12.3 and 12.4) (pdf)Download

U1 L3 Completed Class Notes (12.5) (pdf)Download

U1 L4 Completed Class Notes (12.6) (pdf)Download

Solutions to Quiz Problems (YouTube Playlist)

This semester, I wanted to provide solutions to the quiz problems in the form of a video, so that students could watch me working the problems, in addition to reviewing the quiz key and comparing it to the feedback I left them on their quizzes. The provided solutions videos to date are linked here. This is a playlist...If you click on the lines in the the top right-hand corner, you'll see a drop down menu with all of the videos posted on this playlist to date, listed by course standard.

Fall 2019 Quiz Keys

I use standards based grading in the face-to-face sections of this course. When using SBG, rather than assessing student understanding using tests, I use more frequent quizzes that cover the major topics (called standards) of our course. This course has about 30 standards. The online section covers exactly the same content, with the material assessed through unit exams and a comprehensive final rather than quizzes and a final.

The students are given access to quiz keys so that they can see A-level work, and so that they can familiarize themselves with the format of the quizzes and exams. Students know that I won't simply ask them the same questions with different numbers. Students need a thorough understanding of each standard and the related concepts and techniques in order to be successful.

The first 8 quiz keys have been posted here. The Fall 2019 Quiz 9 key will be posted at a later date. Quiz 10, which covers surface integrals, Stokes's theorem, and Gauss's divergence theorem, is administered as a take-home quiz before the final. The keys to in-class quizzes will be posted here.

Students are encouraged to create one-page 8.5" by 11" formula sheet for each quiz in Calculus III.

Sasha Townsend