Calculus for Everyone

Section A: Wednesdays 3:00-4:30 PM Eastern Time (12:00-1:30 PM Pacific Time)

Calculus for Everyone is a classical approach to mathematics that allows any high school student who has completed a first-year algebra course to learn the fundamentals of calculus. This integrated course examines the history of its development, beginning with the problem of change, and focuses on “the concepts of calculus proper” (Stokes, 2020, p. xvii), encompassing physics and philosophy of motion as well as “real calculus: derivatives, integrals, limits, and the Fundamental Theorem of Calculus” (p. xxvi).

This class is divided into four eight-week quarters. Students will be assigned readings, lectures, exercises, and quizzes, emphasizing both the history of the development of calculus and the mathematical knowledge of limits, derivatives, and integrals. In the convention of the flipped-classroom model, students will complete assignments before attending the weekly 1.5-hour live recitation (note: two weeks will be asynchronous discussions.) Each quarter will end with an exam testing the material covered in that quarter, with the exception of the final quarter which will end with a comprehensive final exam.

Course Prerequisite and Sequencing:

Prerequisite: The successful completion of Algebra I

This course is ideal for students who:

• Are seeking a classical approach to Calculus.
• Value an historical approach that integrates mathematics with natural philosophy.
• Want to understand real-life applications for Calculus.
• Are STEM minded, Liberal Arts minded, or both.
• Are unsure if they would like to take a Calculus course.
• Have decided to take Calculus at some point.

Calculus for Everyone may be taken before, after, or alongside Geometry but should not be taken at its expense. It is not a substitute for Pre-Calculus (Trigonometry) nor is it equivalent to AP/collegiate Calculus I. Rather, by avoiding the "mire" of transcendental functions, it provides foundational skills and understanding, giving crucial perspective to philosophy, science, and mathematics. Dr. Stokes asserts, “CALCULUS ISN'T A LUXURY ... Until our students learn the fundamentals of calculus and Euclid’s Elements, they’ll never integrate mathematics with the rest of their studies, and therefore they’ll never really understand the whole” (p. xxvi).

Curriculum:

(discount available for students through Roman Roads Press)

Optional Resources:

Adler, M., & Van Doren, C. (1972). How to Read a Book: The Classical Guide to Intelligent Reading. Touchstone, Simon and Schuster.

Kern, A., & Lipinski, A. (2017). A CiRCE Guide to Reading. CiRCE Institute.

Lehman, J. (2021). Socratic Conversation: Bringing the Dialogues of Plato and the Socratic Tradition into Today’s Classroom. Classical Academic Press

Woods, R. (2019). Mortimer Adler: The Paideia Way of Classical Education. Classical Academic Press. ‌

Course Objectives:

Throughout the course, students will:

1. Learn about the need for calculus and its historical development.
2. Learn the general concept of function and its applications to real-world situations.
3. Learn to work with algebraic functions and their applications in applied problems.
4. Learn the concepts of the derivative and its underlying concepts.
5. Learn to calculate derivative for various type of functions using definition and rules.
6. Apply the concept of derivative to completely analyze graph of a function.
7. Learn about various applications of the derivative
8. Learn about anti-derivative and the Fundamental Theorem of Calculus and its applications.
9. Learn to use concept of integration to evaluate geometric area and solve other applied problems.

General Information for the Virtual Classroom:

• Stable internet connection
• Working webcam, headset, and microphone
• Ability to convert written work into clear, readable portable document format (pdf)

References:

Stokes, M. (2020). Calculus for Everyone: Understanding the Mathematics of Change. Roman Roads Press.