Change of Variables & The Jacobian | Multi-variable Integration

You've reached the end of Multi-variable Calculus! In this video we generalized the good old "u-subs" of first year calculus to multivariable case with a multivariable change of variables. The trick is to set up a new coordinate system where the messy region before is now very nice, perhaps just a rectangle. We have to be careful though as we have to multiply our integrands by a scaling factors called the Jacobian. In this video I sketch the intuition behind the Jacobian and compute it out in an example.

****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Multivariable Calculus Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd

****************************************************
Other Course Playlists:

►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m

► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n

►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS

►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Want some cool math? Check out my "Cool Math" Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho

****************************************************
►Follow me on Twitter: http://twitter.com/treforbazett

*****************************************************

This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join

MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett

Видео Change of Variables & The Jacobian | Multi-variable Integration канала Dr. Trefor Bazett