3D Interactive Plots for Multivariate Calculus

Abstract

In this book, you will find a pool of interactive and colorful 3-dimensional (3D) graphs with supplemental self-checking questions. The topics covered in this book have been selected to improve both teaching and learning vital concepts and techniques in multivariable calculus, one of the fundamental courses across the undergraduate curriculum in science and engineering.

The 3D graphs in this resource were developed using an open-source graphing tool (Geogebra). The units in this resource have been organized based on the most used open-source textbook in this subject area, “Calculus Volume 3” by OpenStax3, to ensure both learners and instructors have free access to a high-quality open education resource (OER) in this area that is accessible and inclusive by design.

This resource was designed to apply learner-centered design principles, aiming to (a) engage diverse learners and develop their geometric intuition about abstract and complex mathematical concepts (e.g., partial derivatives, multiple integrals, vector fields), and (b) train learners to make connections between concepts visually (e.g., connecting “vectors” in mathematics with “magnitude” and “direction” in physics) and thereby prepare them well to understand more fully engineering, physics and mathematical problems (e.g., differential equations) in their subsequent STEM coursework.