Vector Calculus - Lecture 17: Making Use of Green's Theorem скачать в хорошем качестве

Vector Calculus - Lecture 17: Making Use of Green's Theorem

We work through several example problems involving Green's theorem. In particular, we use Green's theorem to compute areas via vector line integrals, volumes via vector line integrals, and vector line integrals (even over non-closed curves) via double 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 16: Introduction...   Next lecture:    • Vector Calculus - Lecture 18: How to Think...   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: Area of an ellipse via Green's theorem: https://www.desmos.com/calculator/bga... Double integral under a cycloid: https://www.desmos.com/calculator/tzm... Double integral under a cycloid (as a volume): https://www.desmos.com/3d/cv9v9q3snc Ugly vector line integral, saved by Green's theorem: https://www.desmos.com/calculator/z7c... Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction 01:02 - Computing areas via vector line integrals 06:15 - Computing double integrals (volumes) via vector line integrals 16:11 - Computing vector line integrals via double integrals #vector_calculus #greens_theorem #line_integral