Introduction

The Purpose of This Resource

In this book, you will find a pool of interactive and colorful three-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.

What to Expect

Within each unit, you’ll find the following sections:

• The Concept: In this section, we’ll share the key concepts you’ll need to know for the unit topic.
• The Plot: In this section, we’ll provide step-by-step instructions on engaging with a 3D plot related to the unit topic. Following the instructions, you should be able to manipulate the 3D graph to understand the key concepts for the unit.
• Self-Checking Questions: In this section, you’ll find questions to test your understanding of the unit concepts. Answers to some of the questions will be provided; however, some questions will only be able to be found through using the 3D plot in the unit.