Vector Calculus - Lecture 10: Scalar Line Integrals (Examples and Other Interpretations)

Описание: We demonstrate how to compute scalar line integrals, and we talk about a few physical interpretations of them; as accumulating density into total mass, and as the area of a 2D region in 3D space.

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 9: Scalar Line I...  
Next lecture:    • Vector Calculus - Lecture 11: What is a Ve...  

Blank course notes (lectures 8-10): https://njohnston.ca/vector_calculus/...
Annotated course notes (lectures 8-10): https://njohnston.ca/vector_calculus/...

Desmos graphs used in this video:
Line integral along an intersection of surfaces: https://www.desmos.com/3d/vhnhpkcq6j
Line integral along a wire: https://www.desmos.com/calculator/lu1...
Line integral as area of a surface: https://www.desmos.com/3d/szhweovvnq
Area under a surface along a curve: https://www.desmos.com/3d/vaz1uoxuhp

Please leave a comment below if you have any questions, comments, or corrections.

Timestamps:
00:00 - Introduction
00:37 - Scalar line integral along the intersection of two surfaces
07:01 - Scalar line integral of density is mass
13:26 - Scalar line integrals for computing 2D areas in 3D space

#vector_calculus #lineintegral #line_integral