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This video aims to introduce green's theorem, which relates a line integral with a double integral.
Line Integrals: https://youtu.be/dnGDmZynvYY
Divergence and Curl by 3b1b: https://youtu.be/rB83DpBJQsE
For the example at 5:07, the equation of the vector field has the x equation and y equation flipped. It should be F=(-yx + x^3, 6y-9x).
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Read More:
https://brilliant.org/wiki/greens-theorem/
https://mathinsight.org/greens_theorem_idea
https://www.khanacademy.org/math/multivariable-calculus/greens-theorem-and-stokes-theorem/greens-theorem-articles/a/greens-theorem
http://tutorial.math.lamar.edu/Classes/CalcIII/GreensTheorem.aspx
#calculus #multivariable #greenstheorem
Music by Chillhop: http://chillhop.com/listen
This video was animated using manim: https://github.com/3b1b/manim
Source code for the animations: https://github.com/vivek3141/videos