Vector Calculus - Lecture 1: Paths and Curves

We start our study of vector calculus and vector-valued functions by exploring paths: functions from (an interval in) R to R^n. We illustrate a few examples in R^2 and R^3 and we discuss how to interpret and think about paths and the curves that they trace out.

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/...

Next lecture:    • Vector Calculus - Lecture 2: The Velo...  

Course notes: coming soon

Desmos graphs used in this video:
Line path: https://www.desmos.com/calculator/vda...
Helix path: https://www.desmos.com/3d/whnwtqtirc
Weird circle parametrization: https://www.desmos.com/calculator/6qr...

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

Timestamps:
00:00 - Introduction
03:21 - Paths
07:50 - A line path
10:52 - A helical path
13:42 - A weird circle path
20:22 - Paths versus curves

#vector_calculus #paths #curves