We provide some intuition for Green's theorem by showing that it says that the accumulation of counterclockwise rotations in a region equals the counterclockwise rotation around the boundary of the region.
Textbook: "Vector Calculus" by Susan J. Colley and Santiago Cañez
Canada link: https://www.amazon.ca/dp/B09M8DL4TJ/&tag=veccalc06-20
USA link: https://www.amazon.com/dp/B09M8DL4TJ/&tag=veccalc-20
Vector Calculus playlist: https://www.youtube.com/playlist?list=PLOAf1ViVP13haWs-MkyL9u_r8pMgFoWT6
Previous lecture: https://youtu.be/-ApUxVtz5XQ
Blank course notes (lectures 16-19): https://njohnston.ca/vector_calculus/week5.pdf
Annotated course notes (lectures 16-19): https://njohnston.ca/vector_calculus/week5_annotated.pdf
Desmos graphs used in this video:
Green's theorem via counterclockwise rotations: https://www.desmos.com/calculator/sqbmsi5tea
Please leave a comment below if you have any questions, comments, or corrections.
Timestamps:
00:00 - Introduction
01:04 - The vector line integral in Green's theorem
02:13 - The double integral in Green's theorem
#vector_calculus #greens_theorem #line_integral