Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated Integrals
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- เผยแพร่เมื่อ 28 ส.ค. 2024
- Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated Integrals: The techniques of solving Double Integrals with a focus on how to construct a double integral over a given region.
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I am a 56-year-old person with an MFA. My dream was to become an astrophysicist, but during my teens, my math teachers were awful. I was traumatized. Fast forward 45 years later, Prof Leonard came 😀into the grand scheme of things, and now I aim to apply to MIT for my degree in theoretical physics. I teach myself and never tire of watching this guy teach us new tricks. Thank you!
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It's math. It's not like it ever changes! :)
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Thanks very much! And yes, it does motivate me :)
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Context: Integrating under regions. What is R, how to find R, and how to evaluate when not given R (how to find)
2:06 check f(x,y) is a surface.
3:10 doesn't matter which order you find under the region dx, or dy, still yields same area.
where R is the Rectangular Region, which remember is based on the change in X and Y which both have intervals. Thus.
a
3:01:05 Change of Order of Integration
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To be fair, it's a 3 hour lecture.
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Actually, it does last 3 hours because sometime he would use up his 3 hours of time in the last video/section. You know this when sometimes his cloth from the last video is the same at the beginning of the following video. Until 3 hours pass, he cuts the video wear new cloth meaning is the next day.
Same here, mine did all of this (including polar coordinates) in 2 hours, and he looks angry all the time, mutters and barely interacts with the class. So boring. Leonard is like a God in comparison
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More than half the people in my lecture don't show up to class and they just watch Professor Leonard instead
Its what I started doing in my current class lol
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Almost all my math teachers have been those super-formal and boring types who have stood and mumbled theorems and proofs throughout the entire lectures and hardly given any example problems and never talked to the students.
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When he asks the class "raise your hand if you understand this" I put my hand up as if I was in class, and I answer his questions out loud. Anyone else?
+Deasert Fox i am also guilty
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guilty
Yup
head nod if you understand what's happening here
Thank god that I finally found a professor that doesn't assume that everyone in a calc iii lecture already understands how to set these integrals up... thanks for the great video!
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At the time of writing, this video was uploaded 7 years ago, but it still continues to help students like me, and we all greatly appreciate it
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Thank you sir. Spent exactly 6 hours taking notes with you. If anyone is just watching without taking notes I highly recommend taking notes, I've tried both and I found that I grasp the idea much better when I'm taking notes rather than just watching.
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Due to the pandemic we are doing online lectures as any other Uni, but the Calculus Class just isn't woeking for me personally. My professor did not explain how to set up the intergralls either, rather just gave it and expected us to simply know how to do it. When i asked them how to do it they gave me a very vague answer that didn't help at all. Thank your professor Leonard for uploading these videos back in 2016, you are helping me so much right now.
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if one variable is dependent on the other, that's gonna be the inner variable [to realise that, draw the region]
if both variables lie in a constant range (one number to another), the inner variable will be the one wrt to which it's easier to evaluate the integral the first time
if you aren't clear on which one should be the lower and upper bound for the dependent variable, draw the region
2:39:52
in problems, replace the third variable (usually z) by f cause that's your function
sometimes you will have to forcefully change bounds cause you can't integrate easily [dx dy]
{going along dy is travelling parallel to y axis}
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Why in the world would anyone call it "poor notation" to explicitly write out the variables for the upper and lower bounds in the integrals?
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and waiting...
*waits and cries about differentials next semester without our youtube professor*
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I hope that you make videos for those sections during the next 5 weeks.
1-Vector Fields->Vector and Scalar Fields- Consevative Fields - Line integrals - Surface and surface integrals - Oriented Surfaces and Flux integrals.
2-Vector Calculus->Gradient, Divergence and Curl-Green's Theorem in the Plane - The Divergence Theorem in 3 space - Stocks's Theorem - Orthogonal Curvilinear Coordinates.
Thanks a lot :) Professor Leonard
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Professor,
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i want to take the time and say thank you very much for your videos professor Leonard! i am currently taking calculus 3 and i have to say that i am learning more about vectors, partial derivatives, and now double integrals than my professor whom is teaching my class. you do an outstanding job explaining the information from the fundamental principals and thats what i enjoy most about your lectures. i can see that you truly care about your students. i wish my university had ten more like you! i appreciate your hard work, keep up the good work. i hope in the near future you can upload more lectures covering topics in Linear Algebra and Differential Equations.
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you do a great job of instructing on the mechanics of how to do a double integral! sometimes i have a hard time remembering though the underlying logic of how partial derivatives taken one at a time are giving the overall volume.
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Your colored line example was very helpful in conceptualizing how to set up integrals!
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1:27:00 - 1:28:00
He took 1 min to explain what I didn't get in last whole lecture
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other calc teachers most likely