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.

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

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[aadi.p]

Can I report this video for too eye opening

[imanabu]

Quarantine isn't that bad when we have people like you helping us out, thanks much 🌸🌸🌸

[pbillings]

Greatly appreciated the second half as to WHY the Jacobian comes into play!

[mockingbird]

When you're a visual learner, videos like this are an absolute godsend

[Chomusuke]

The Jacobian part in the end is pure gold

[abhinavhampiholi]

I had taken multivariable calculus a couple of years ago and needed a refresher. This was great!

[lancelovecraft]

Excellent vid my friend. I took multivariable calc years ago and never really understood the jacobian or its purpose. Your explanation made it so simple and obvious. Thank u

[maulaahmad]

I was banging my head trying to understand the jacobian cuz it was introduced with the chain rule topic in my school. This video just made it very easy to undertand now. Thank you very much

[GoutamDAS-lswb]

Thank you Professor Bazett for an excellent video on the Jacobian. I am taking Multivariable Calculus (II) right now on edX offered by MIT but I always return to your videos because of your clear and lively teaching style. I look forward to many more. You make the videos entertaining as well!

[ProCelestialEmpire]

Thanks a lot Dr. Bazett! I searched many materials and so far to me you are the only one that made the vectors transform part clear. Subscribed.

[PinakCborty]

This is one of the most beautiful explanations on the intuition behind Jacobian I have come across on youtube. Thank you.

[AmitKumar-udyq]

Never found mathematics this much interesting.. Thank you for all the efforts you have made for us sir.# respect

[tomatrix]

This was absolutely top class as far as an explanation on an advanced topic can be. Great

[chartered]

I was about to google to find out the reason why we needed the Jacobian, your video presented is so beautifully it can't be beaten!!. Thank you so much !!

[walac]

Man, I was struggling to understanding the reasoning behind the Jacobian, but your video provided me the insight thanks a lot!

[briandwi]

That was the last one of the whole series on Calculus 3. I watched every one and they were brilliant. Thanks for all the insights.

[jonasfarbo]

The motivation for the Jacobian explained with the u-substitution method from calculus 2 was very helpful for my intuition behind this topic. Thank you.

[Harry-ubfv]

That one dislike is given by a man who didn't even know the single variable calculus. Awesome explanation Sir!❤

[proxy]

You are so good at explaining the intuition of things. You are a great teacher, thank you.

[Harry-ubfv]

This channel doesn't make me feel that I'm quarantined at home.:)