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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