Mastering Change of Variables & Jacobian in Multivariable Integration đ
Learn how to extend substitution techniques to multiple variables with the Jacobian. Perfect for conquering multivariable integrals and advancing your calculus skills!
Dr. Trefor Bazett
377.5K views âą Dec 18, 2019
About this video
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.
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YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
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âșFull Multivariable Calculus Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âĄâĄâĄSUPPORT THE CHANNELâĄâĄâĄ
âșSupport on PATREON: https://patreon.com/DrTrefor
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COURSE PLAYLISTS:
âșDISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
âșLINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
âșCALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
âșCALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
âșMULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âșVECTOR CALCULUS (Calc IV): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
âșDIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
âșLAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âșGAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
âșCool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
âșLearning Math Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
âșLaTeX: https://www.youtube.com/watch?v=-HvRvBjBAvg&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&index=2&ab_channel=Dr.TreforBazett
SOCIALS:
âșX/Twitter: http://X.com/treforbazett
âșTikTok: http://tiktok.com/@drtrefor
âșInstagram (photography based): http://instagram.com/treforphotography
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
âșFull Multivariable Calculus Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âĄâĄâĄSUPPORT THE CHANNELâĄâĄâĄ
âșSupport on PATREON: https://patreon.com/DrTrefor
âșMATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett
âșCURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes
COURSE PLAYLISTS:
âșDISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
âșLINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
âșCALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
âșCALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
âșMULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âșVECTOR CALCULUS (Calc IV): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
âșDIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
âșLAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âșGAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
âșCool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
âșLearning Math Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
âșLaTeX: https://www.youtube.com/watch?v=-HvRvBjBAvg&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&index=2&ab_channel=Dr.TreforBazett
SOCIALS:
âșX/Twitter: http://X.com/treforbazett
âșTikTok: http://tiktok.com/@drtrefor
âșInstagram (photography based): http://instagram.com/treforphotography
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Video Information
Views
377.5K
Likes
10.4K
Duration
10:07
Published
Dec 18, 2019
User Reviews
4.8
(75)