Defining Double Integration with Riemann Sums | Volume under a Surface
We generalize the ideas of integration from single-variable calculus to define double integrals. The big idea in single variable calculus was to chop up the region into a sum of little rectangles called the Riemann sum which was an approximation for the area under a function. Then we took a limit of the Riemann sum to define the definite integral. We do much the same here, looking to find a formula for the volume under a surface. Now a rectangular region in the domain is broken up into a lot of little prisms and the sum of those volumes is the Riemann sum. Take the limit as the sizes in that partition goes to zero and this defines a double integral.
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Видео Defining Double Integration with Riemann Sums | Volume under a Surface канала Dr. Trefor Bazett
****************************************************
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:
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Видео Defining Double Integration with Riemann Sums | Volume under a Surface канала Dr. Trefor Bazett
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