3d curl formula, part 2  Summary and Q&A
TL;DR
The video explains the formula for threedimensional curl, using determinants to derive a vectorvalued function that corresponds to the curl.
Questions & Answers
Q: What is the role of determinants in computing the vectorvalued function for the curl?
Determinants are used to compute the vectorvalued function for the curl by multiplying partial derivatives of the multivariable function and subtracting them according to the determinant rule.
Q: Does the formula for threedimensional curl have any connection to twodimensional curl?
Yes, the formula for threedimensional curl shares similarities with the twodimensional curl. The Kcomponent of the formula represents the twodimensional curl, while the other components correspond to rotation in different planes.
Q: Is it necessary to memorize the entire formula for threedimensional curl?
No, it is not necessary to memorize the entire formula. By remembering that curl is represented as Del cross V, the process of deriving the formula can be applied to any vectorvalued function.
Q: How can the formula for threedimensional curl be applied in practical contexts?
The formula for threedimensional curl can be used to analyze the rotation and circulation of vector fields in threedimensional space. It is applicable in various physics and engineering applications.
Summary & Key Takeaways

The video explains the process of computing the determinant of a threebythree matrix to derive a vectorvalued function for the curl.

The determinant involves multiplying partial derivatives of the multivariable function with respect to different variables and subtracting them.

The formula for threedimensional curl can be represented as the cross product between the Del operator and the vectorvalued function.