3d curl formula, part 2 | Summary and Q&A

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May 27, 2016
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Khan Academy
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3d curl formula, part 2

TL;DR

The video explains the formula for three-dimensional curl, using determinants to derive a vector-valued function that corresponds to the curl.

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Questions & Answers

Q: What is the role of determinants in computing the vector-valued function for the curl?

Determinants are used to compute the vector-valued function for the curl by multiplying partial derivatives of the multi-variable function and subtracting them according to the determinant rule.

Q: Does the formula for three-dimensional curl have any connection to two-dimensional curl?

Yes, the formula for three-dimensional curl shares similarities with the two-dimensional curl. The K-component of the formula represents the two-dimensional curl, while the other components correspond to rotation in different planes.

Q: Is it necessary to memorize the entire formula for three-dimensional 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 vector-valued function.

Q: How can the formula for three-dimensional curl be applied in practical contexts?

The formula for three-dimensional curl can be used to analyze the rotation and circulation of vector fields in three-dimensional space. It is applicable in various physics and engineering applications.

Summary & Key Takeaways

  • The video explains the process of computing the determinant of a three-by-three matrix to derive a vector-valued function for the curl.

  • The determinant involves multiplying partial derivatives of the multi-variable function with respect to different variables and subtracting them.

  • The formula for three-dimensional curl can be represented as the cross product between the Del operator and the vector-valued function.

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