Vector Calculus - Lecture 21: Conservative Vector Fields and Path Independence скачать в хорошем качестве

Vector Calculus - Lecture 21: Conservative Vector Fields and Path Independence

We present a theorem that says that a vector field has path-independent line integrals if and only if it is a gradient field. 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 20: What is Path...   Blank course notes (lectures 20-23): https://njohnston.ca/vector_calculus/... Annotated course notes (lectures 20-23): https://njohnston.ca/vector_calculus/... Desmos graphs used in this video: Line segment and parabolic arc example: https://www.desmos.com/calculator/mt6... A non-path-independent example: https://www.desmos.com/calculator/uql... Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction 00:46 - The main theorem 08:18 - Our first example 10:58 - A non-conservative example #vector_calculus #line_integral #path_independence