Uploaded July 2020 | Updated September 2026, 1 week ago
Vector field line integrals: youtu.be/0TC4QEE56oc
In-depth explanation of curl formula: youtu.be/W--29EqUSl0
Intuition and explanation of the meaning of curl in terms of line integrals and how a vector field changes as it moves. We'll also give an overview of the derivation for the curl formula!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
0:00 Understanding Curl
6:16 Curl in 3 Dimensions
8:55 Formula Intuition
New math videos every Monday and Friday. Subscribe to make sure you see them!
Music: C418 - Pr Department
Vector field line integrals: youtu.be/0TC4QEE56oc
In-depth explanation of curl formula: youtu.be/W--29EqUSl0
Intuition and explanation of the meaning of curl in terms of line integrals and how a vector field changes as it moves. We'll also give an overview of the derivation for the curl formula!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
0:00 Understanding Curl
6:16 Curl in 3 Dimensions
8:55 Formula Intuition
New math videos every Monday and Friday. Subscribe to make sure you see them!
Music: C418 - Pr Department

![Induction on Real Numbers
Video on supremum: https://youtu.be/o0TksrG5OsY
Paper on real induction: https://arxiv.org/pdf/1208.0973
Proof by induction is often taught as something that only works for integers, natural numbers, or whole numbers. However, theres an analogous concept to induction that applies to intervals on the real numbers, even though the real numbers are an uncountable set! This video explains and proves the result for the interval [0,1], which can be generalized to arbitrary closed intervals in the real numbers.
Topology playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJEGnUPxM1KUVOHkW4kN6QU_
0:00 The Theorem
4:36 Proof
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Music: C418 - Smooth Fall Induction on Real Numbers](https://i.ytimg.com/vi/bXTbGJxW_fE/mqdefault.jpg)








