Course Overview
These resources are designed to support students in Calculus III through a combination of lecture notes, companion videos, and interactive visualization tools focused on multivariable thinking.
A major emphasis of the course is developing geometric intuition and the ability to visualize mathematical objects in three dimensions.
Lecture Notes
Structured lecture notes covering vectors, surfaces, partial derivatives, multiple integrals, vector fields, and vector calculus.
Video Resources
Complete lecture videos and shorter topic-specific videos designed to accompany the Calculus III notes, reinforce key concepts, and provide additional worked examples.
AR Visualizer
A beta augmented reality tool for exploring Calculus III objects such as surfaces, curves, vectors, and other three-dimensional structures.
Developed in collaboration with Notre Dame’s Office of Digital Learning to help students build geometric intuition beyond the static page.
Lecture Notes
Student lecture notes and corresponding solution versions organized by unit. Click a unit below to expand the topic list.
Unit 1: Vectors and Geometry of Space
Unit 2: Space Curves and Multivariable Functions
Unit 3: Optimization
Unit 4: Multiple Integrals and Applications
Unit 5: Vector Fields and Vector Calculus Theorems
Video Resources
These video collections are intended to support the lecture notes above. The full-length lectures are approximately 50-minute class sessions that follow the notes closely, while the topic-specific videos offer shorter explanations and examples for targeted review.
Complete Lecture Videos
Full class-length Calculus III lectures that serve as companions to the written notes. These are especially useful for students who want to review an entire lesson from start to finish.
Topic-Specific Videos
First Edition, shorter videos focused on individual Calculus III topics, examples, and techniques. These were created with Edward Burkard, PJ Jedlovec, and Ben Lewis.
Collaborators
These videos were developed over time with colleagues and friends who have contributed to Calculus III instruction and student support.