This is a killer video for people that do not understand where Green’s theorem comes from. Since I understood it since the 10th grade the speed did not kill it for me, but you may want to make a second video slowing down and explaining this at a level for people that are not math heads. To be honest with you this video should have thousands of times the likes, but I think “ the level” this is presented at holds it back from exploding. I am NOT saying to get remove this video, because this what some people need also. Hope I said this right and this is not taken as a being critical of the absolute Beautiful job you did.
Please provide a reference for the definitions of "type 1" and "type 2" regions ... I certainly wish you were one of my instructors as a math undergrad student back in the Early Bronze Age ...
that's on the wikipedia page @Bulldawg. What I don't understand is how you go from having a proof for type 1 region for part A and a proof of type 2 region for part B to having a proof of A+B for type 3.
I had this same doubt. Reading the comments I got it. The huge simplification he made at the beginning of the video was that D is a simple region, so you can express the region as a x-simple and y-simple. The regions are the same
Great Work , Thank you very much. I have a question, is it allowable to add the left sides and the right sides of both equations at the end of the video?, since the regions are not the same (The D in the first equation is not the D in the second), in the first it's a type 1 while in the second it is a type 2, so they can't be the same unless the region is a rectangle, so how can we add integrals with different regions of integration (even if the integrands are the same)??
You've spotted the *huge* simplification he made and glossed over: right at the start, he said D is *both* a type 1 and type 2 region - i.e. as you point out, a rectangle. Made it seem like it was much more general a proof than it actually was!
I thought about this some more and am super happy to say I was wrong. A rectangle certainly is both type 1 + 2, but there are other regions which satisfy both constraints that are _not_ rectangles: for example, a circle.
I believe the argument can be made that by approximating the area as small rectangles it applies to any shape as long as the variable of integration tends to 0, just as an integral is a approximation of small rectangles with width dx->0 @@cjp39
The reason that Type 1 + Type 2 doesn't necessarily imply rectangle is that the "straight" sides are allowed to have zero length and the proof still works.
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I can’t believe how many quality videos that you have been consistently putting up ever since I got to know you! Thank you!
Thanks, I am also thankful for those shoutouts from you early on that really helped boost my channel!
I agree. Hard problems explained simply. This is how maths should be.
This is a killer video for people that do not understand where Green’s theorem comes from. Since I understood it since the 10th grade the speed did not kill it for me, but you may want to make a second video slowing down and explaining this at a level for people that are not math heads. To be honest with you this video should have thousands of times the likes, but I think “ the level” this is presented at holds it back from exploding. I am NOT saying to get remove this video, because this what some people need also. Hope I said this right and this is not taken as a being critical of the absolute Beautiful job you did.
Good suggestion 👍.
Turns out that I have learnt to get used to his speed and it's now boring if he is slow 😂.
You have become my go-to for all things math.
Great job!
I was stuck at the proof of Green's theorem, now I totally understand it...Thanks 🙏
Please provide a reference for the definitions of "type 1" and "type 2" regions ... I certainly wish you were one of my instructors as a math undergrad student back in the Early Bronze Age ...
that's on the wikipedia page @Bulldawg. What I don't understand is how you go from having a proof for type 1 region for part A and a proof of type 2 region for part B to having a proof of A+B for type 3.
I had this same doubt. Reading the comments I got it. The huge simplification he made at the beginning of the video was that D is a simple region, so you can express the region as a x-simple and y-simple. The regions are the same
You can go to Vector Calculus of Marsden to see the definitions, for example.
@@A_Helder16 i think marsden dont provide the proof of the theorem.
Great Work , Thank you very much.
I have a question, is it allowable to add the left sides and the right sides of both equations at the end of the video?, since the regions are not the same (The D in the first equation is not the D in the second), in the first it's a type 1 while in the second it is a type 2, so they can't be the same unless the region is a rectangle, so how can we add integrals with different regions of integration (even if the integrands are the same)??
You've spotted the *huge* simplification he made and glossed over: right at the start, he said D is *both* a type 1 and type 2 region - i.e. as you point out, a rectangle. Made it seem like it was much more general a proof than it actually was!
I thought about this some more and am super happy to say I was wrong. A rectangle certainly is both type 1 + 2, but there are other regions which satisfy both constraints that are _not_ rectangles: for example, a circle.
I believe the argument can be made that by approximating the area as small rectangles it applies to any shape as long as the variable of integration tends to 0, just as an integral is a approximation of small rectangles with width dx->0 @@cjp39
The reason that Type 1 + Type 2 doesn't necessarily imply rectangle is that the "straight" sides are allowed to have zero length and the proof still works.
Sach a simple proof thank u Professor ♥️😘love from Pakistan 🇵🇰
Simply astounding 👏
Can you do something on Jordan measure? I dont quite get what it is supposed to tell me.
Thx for your vids . They are great
Hat's off. I really love real Math, proof, proof and proof. Application is too boring for me once concepts well understood.
Thank you math Sting
Good job everything wery well i wish good luck you
Thank you
#YEET