Vector Calculus - Lecture 16: Introduction to Green's Theorem скачать в хорошем качестве

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/&... USA link: https://www.amazon.com/dp/B09M8DL4TJ/... Vector Calculus playlist:    • Vector Calculus   Previous lecture:    • Vector Calculus - Lecture 15: Examples and...   Next lecture:    • Vector Calculus - Lecture 17: Making Use o...   Blank course notes (lectures 16-19): https://njohnston.ca/vector_calculus/... Annotated course notes (lectures 16-19): https://njohnston.ca/vector_calculus/... Desmos graphs used in this video: Scalar line integrals are path-independent: https://www.desmos.com/calculator/5ls... Vector line integrals are path-independent (except for orientation): https://www.desmos.com/calculator/oql... Green's theorem example as a vector line integral: https://www.desmos.com/calculator/0c0... 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