Vector Calculus - Lecture 16: Introduction to Green's Theorem

We introduce Green's theorem, which shows that double integrals can be computed via vector line integrals and vice-versa. We also discuss what the "orientation" of a curve refers to, and why it matters when computing vector line integrals (but not scalar line integrals). 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/sz6_v4979W8 Next 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: Scalar line integrals are path-independent: https://www.desmos.com/calculator/5lsji8fu0a Vector line integrals are path-independent (except for orientation): https://www.desmos.com/calculator/oqlnjic0yl Green's theorem example as a vector line integral: https://www.desmos.com/calculator/0c0yhdfefu Green's theorem example as a double integral: https://www.desmos.com/3d/h9nbjcev65 Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction and statement of theorem 02:50 - Discussing notation and hypotheses of the theorem 09:20 - Orientation of a curve and why it matters 13:51 - Example: verifying Green's theorem #vector_calculus #greens_theorem #line_integral