Materials for Analytic Geometry & Calculus III
A Work-in-Progress
These are materials I used in Calculus III during a recent semester. There are some errors in these documents. I'll update the documents soon! Check out the links on this page to see recent syllabi, SBG course standards and rubric, course notes, completed course notes, and quiz keys from a recent semester.
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, in face-to-face sections, 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. Online courses are handled differently. I use standards based grading in the face-to-face sections, and an online version of SBG for the online sections. Lectures focus on derivations, computation, and meaning.
I hope you find multivariable calculus as beautiful as I do!
Prerequisite Review Materials
There's so much that we're building upon in Calculus III. If you need review materials, please view the materials on the corresponding pages on this site.
If you're unable to find a resource because I haven't yet uploaded it, let me know, and I'll be happy to find and upload it, or direct you to other online resources.