The Jacobian Matrix (concept and derivation)

This is an interesting derivation of the Jacobian matrix that I worked out and wanted to share. I am not a mathematician, although I nearly have a bachelor's in applied mathematics. For this reason, I would like to make it clear that some of my terminology or methods may not be proper. This video will likely be useful for those of you, especially physics or engineering majors, that like to see "under the hood" as opposed to just "driving the vehicle".

[@juanlocabrera4139]

I am a mechanical engineer studying robotics. All the books I've consulted talk about the Jacobian, but none of them really explain how it works or what lies behind it, and how it relates to linearizing nonlinear functions. Your level of detail is fantastic; keep it up!

[@nishchayy]

This is super useful for me , thank you so much for this video . I found no where this much clear derivation of Jacobian. Kudos to you.

[@understandingmathandphysic9438]

@@nishchayy I think sometimes the simplicity of math gets hidden behind a curtain of complexity. Most of the math I’ve learned is just linearization using calculus, the Jacobian seems no different :)
Thank you for taking the time to watch my video!

[@nishchayy]

@@understandingmathandphysic9438 great words of wisdom.. the one admire mathematics when he see simplicity. . I like the way you explains .. thank you for your videos