Vector Calculus - Lecture 21: Conservative Vector Fields and Path Independence
Автор: Nathaniel Johnston
Загружено: 2025-03-02
Просмотров: 427
Описание:
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
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