Double Integration in Polar Coordinates | Example & Derivation

While Cartesian coordinates are great and all, some regions and some integrands are way nicer when described using polar coordinates. In this video we play around with polar coordinates, derive the formula for double integration in polar coordinates, and see an example. The derivation is much like it was in Cartesian coordinates - a limit of a sum of little volumes - but the geometry of the little volumes change in polar coordinates as they no longer have rectangular bases.

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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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[agh]

Not only are your formula derivations presented extremely logically but your diagrams show exactly where the formulas come into play. The latter is what makes your explanations so much more cogent than others I've seen. It's one thing being able to follow where a formula comes from, making the abstraction to intuit how that formula applies to examples other than that which was used to derive it is the subsequent "jump" where most students falter in their understanding. From videos like yours and those from a select few other youtubers, I've learned to love calculus for the fact that its one of the only branches of math where it's possible to get a complete intuitive understanding of virtually concept without the rigorous mathematical proofs.

[vijaysinghchauhan]

Why I love and appreciate your videos is because you give a clear visual picture.

[SerdceDikarya]

everybody: DOUBLE INTEGRATION Dr.trefor : DOUBLE INTEGEGRATION😎

[Mr.Cele-rkrw]

SUBSCRIBED!! literally serene !!!, , these complex topics kinda used to hurt me but now, they seems tranquility aider cuz of you man, , , , appreciate that.😇

[maryamafzaljutt]

Your videos give a conceptual based geometrical analysis of every topic which is interesting for me

[feafel]

Seriously, I wish I had a teacher like you in my school days

[menoima]

you are just amazing sir and algo sucks deserve many more views

[mono]

Great video! Your explanation is worthy of 1000 likes.

[bhavesh.adhikari]

youtube is tricking me to learn mathematics haha. Great content, just subscribed!

[aymenechchalim]

Can't describe how great you are man, sending love

[jayantachakraborty]

Your explanations are so clear. it is literally helping me a lot. thank you so much...😍

[tasnimsalem]

Your explanation is amazing. Thank you very much. I hope that your videos will open the Arabic translation feature for me because I am Arab and I love the way you explain and your videos and I always study from your channel.❤

[johnholme]

First port of call for an intuitive grasp of mathematics.

[tomatrix]

You’re such a great teacher. Greetings from Ireland Trefor🥂

[ShubhamKumar-qype]

thank you for providing us such a great lecture❤❤

[madanismail]

Man ! Dr Trefor, I am an engineer who studied math, and you're the best one who can break anything big to small, lol Thank you also for the polar curves which BTW are important in Antenna studies, like the smith chart, Thank you so much Dr, I will definitely follow your videos as they are an immense pleasure to watch. Still have Schaum McGraw hill books and Piskounov books as well, lol but also a CAS calculator to help with all this when one doesn't have time.

[jaydean]

Thank you for excellent explanation, I also watched your integration video in 3-D graphing (makes it easy to understand), wish I had access to 3-D graphs when I took calculus (1970's) Thanks

[divishthamalik]

I have my first sem engineering end sem tomorrow your video series was great for a quick revision thanks a lot sir.

[briandwi]

Beautifully clear and concise. Thanks.

[曾华-ds]

Very helpful for me!!! THANK YOU SIR!!