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 |