There’s an exciting addition to the math course catalog this year — though officially called Vectors & Variables, the course is often referred to by students as Multivariable Calculus or “Calculus D,” as the instructor Eric Henry would call it. The course was initially created as an extension of Concord Academy’s Calculus A, B, and C; while it promises the same level of difficulty as other Concord Academy Calculus classes, it dives deeper into the study of calculus by zooming in on specific topics like vectors and parametrics.
Units covered within the course include Vectors & Geometry of Space, Vector-Valued Functions and Motions in Space, Partial Derivatives, Multiple Integrals, Integrals & Vector Fields, and Second-Order Differential Equations. The fact that Vectors and Variables is a brand-new course, coupled with these units, may make the course seem intimidating. Henry has shown incredible flexibility in his lectures; however, he can often be seen fixing the course load based on his students’ voices. “This is my first year teaching this class, as it is all of you who are learning the material for the first time. Please let me know if I am moving too fast,” he says.
While the prerequisites for Vectors & Variables do not include Calculus C, a few of the concepts used within the course require the knowledge; thus, Henry gives students an opportunity to instruct peers who are unfamiliar with concepts. Ranging from arc length to the Taylor and Maclaurin series, a variety of Calculus C basics are taught by peers presenting in front of the class, an approach previously unseen in any other math classes. Moreover, Henry provides the students with an abundance of extra resources afterwards to learn, review, and practice previous calculus concepts, which are most certainly helpful to refresh empty-slated students coming back from summer break.
Another difference of this course is that, unlike other CA’s math courses, Vectors & Variables does not base itself on a CA-issued workbook; rather, it uses Pearson’s 1000+ page text, Thomas Calculus: Early Transcendentals, 15th edition. “It is comprehensive,” says Henry. “Most of the important theorems are proven, and the proofs are well delivered and accessible. [It provides us with a] coherent presentation of the content and a comprehensive reference.” Though he did mention the necessity of editing and adding content, the detailed explanations and colorful, visual representations of 3D planes that are difficult to visualize make the text effective in instructing students who are taking their first steps out of single variables into the world of multivariate calculus.
Henry also integrates black & white video lectures by Herb Gross, a previous MIT professor at MIT’s Center for Advanced Engineering Studies. Gross helps to break down difficult concepts into easy and small pieces to digest; despite the age of the videos, they prove to be extremely helpful to explain with a different perspective in mind. Moreover, similar to discussion-based English and history classes of CA, much of the course revolves around group work and working together with peers on a whiteboard. “[It’s a] departure from a traditional course structure,” Henry said. “ [The approach is] justified by research into learning, particularly mathematical learning.”
While some of the course’s content and structure still remain uncertain, the class looks promising as an upcoming steady-seller Advanced Math topic at CA. It is one of the rare courses that dives much deeper into courses taken previously for two or three semesters and intertwines real-world situations with abstract mathematical concepts. All in all, it is the first advanced math course that contains plausible real-life applications, making it more intriguing and helpful in daily life.