Uploaded July 2020 | Updated September 2026, 1 week ago
Video on scalar field line integrals: youtu.be/WVQgEeZY_l0
Vector field line integrals: youtu.be/0TC4QEE56oc
Video on double integrals: youtu.be/9AHXnRpF0n8
An explanation of how to calculate surface integrals in scalar and vector fields. We go over where the formulas come from and how to actually get to an answer!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
New math videos every Monday and Friday. Subscribe to make sure you see them!
Timestamps:
0:00 Scalar fields
14:18 Vector fields
Music: C418 - Pr Department
Video on scalar field line integrals: youtu.be/WVQgEeZY_l0
Vector field line integrals: youtu.be/0TC4QEE56oc
Video on double integrals: youtu.be/9AHXnRpF0n8
An explanation of how to calculate surface integrals in scalar and vector fields. We go over where the formulas come from and how to actually get to an answer!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
New math videos every Monday and Friday. Subscribe to make sure you see them!
Timestamps:
0:00 Scalar fields
14:18 Vector fields
Music: C418 - Pr Department
![How the Matrix Characteristic Polynomial is Connected to F[x]-Modules](https://i.ytimg.com/vi/jCt6mR3QtPk/mqdefault.jpg "How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
Rational canonical form: https://youtu.be/q5uj4o0O5R0
Similar matrices isomorphism: https://youtu.be/-ligAAxFM8Y
Intro to F[x]-modules: https://youtu.be/H44q_Urmts0
The characteristic polynomial described by the determinant det(xI-A) is very useful when studying matrices. It turns out that its related to modules as well! Here we show how the characteristic polynomial is related to the module form of an arbitrary matrix.
Ring & Module Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
0:00 Computing the determinant
10:07 Similar matrices have same polynomial
12:40 Proof for a general matrix
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Music: C418 - Pr Department")
