How to use this web page:

• Find the topic you wish to learn about in the "Video" column.
• Click on the "Lecture notes" for that row to find where in the lecture I explain the particular thing that interests you.
• Now click on the video link and go to the relevant part of the video.
• Read the "Mathematician spotlight" links anytime and all the time.

Number	Video	Lecture notes	Mathematician spotlight
1	Lines, curves, cross product	playing with planes	Diana Davis; Dance your PhD video
2	Functions of several variables	colors!!!	John Urschel; podcast interview
3	New coordinates	curvy graph paper	Moon Duchin; article
4	Quadric surfaces	colorful families!	Ralph Gomez; interview
5	Limits	vertical surface parts require care	Emily Riehl; interview
6	Derivatives	slopes if you are an Etch-A-Sketch	Richard Schwartz; Math picture books
7	More on derivatives	creases and cusps are not differentiable	Piper Harron; The Liberated Mathematician blog
8	Higher-order partials	everything up a dimension	Ryan Hynd
9	Chain rule	functions of functions (of functions)	Sarah Koch
10	Directional derivatives	slopes if you are not an Etch-A-Sketch	David Rockoff
11	Gradients	route-planning using calculus	Ron Buckmire and Dean Elzinga; interview
12	Extrema	make your life the absolute best	Radia Perlman
13	Extrema on bounded domains	make your life the best... under constraints!	Kathryn Lindsey; article
14	Lagrange multipliers	the coolest idea in this course	Kwadwo Antwi-Fordjour
15	More on Lagrange multipliers	farming and animal husbandry	Nsoki Mamie Mavinga
16	Double integrals	an integral OF an integral!	Erik Demaine; interview
17	Riemann sums	finding volumes when you don't have the function	Autumn Kent; interview
18	More on double integrals	finding the area of any region	Rodrigo Trevino
19	Changing order of integration	making the impossible, possible	Eriko Hironaka
20	Triple integrals	finding volumes!	Yitang (Tom) Zhang; New Yorker article
21	More on triple integrals	bounds to region; region to bounds	Dusa McDuff; podcast interview
22	Even more on triple integrals	changing triple integral order of integration	Jayadev Athreya; dodecahedron paper
23	Integrals in polar coordinates	translating round things into suitable coordinates	Evelyn Lamb; Roots of Unity blog
24	Change of variables	plus Gauss's clever idea	Colin Adams; interview
25	Cylindrical and spherical integrals	what a tiny box looks like in curvy coordinates	Amie Wilkinson; interview
26	Parametric curves	for houseflies who keep track of their mileage	Federico Ardila; article
27	Vector fields	modeling the wind	Rachel Epstein
28	Divergence and curl	measuring sources, sinks and swirls	Dylan Thurston
29	Scalar line integrals	areas of curvy fences, total charges on wires	Steve Robinson
30	Vector line integrals	how much the wind helps or hurts you	Yajnaseni Dutta
31	Green's Theorem	vector line integrals become double (scalar) integrals!	Pamela Harris; article
32	Conservative vector fields	if you go in a loop, your net elevation change is 0	Harrison Bray
33	Parameterized surfaces	wrapping the plane into a curved surface	Siddhi Krishna; isotopy animation
34	Scalar surface integrals	how to find the area of a decorative fascinator	Henry Segerman; stereographic projection video
35	Vector surface integrals	counting how much krill you'll catch in your net	Katherine Johnson; interview video
36	Stokes's Theorem	turning a vector surface integral into a vector line integral	Edgar Duenez; profile
37	More on Stokes's Theorem	doing magic with theorems	The LGBTQ+ mathematician
38	Gauss's Theorem	the FTC, *two* dimensions up!	Gwyn Coogan
39	More on Gauss's Theorem	closing off those pesky holes	Illya V. Hicks
40	Summary of course	we can integrate all the things over all the things!	Lila Fontes

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