Riemann sums and the definite integral

[@alexramirez5104]

This is one of most clear and effective explanations i've come across on the web or from what i've tried to extract from text books, thanks for posting this!

[@chrisodden]

+Alex Ramirez Thanks, Alex. I'm happy it was helpful.

[@alotan2acs]

Great stuff. No other youtube video is this rigorous yet this simple. Thank you for filling the void.

[@rolandoblestcastillo1673]

A nice and very clear video about the Riemann sums, sometimes being confused with Darboux sums ( 2). Thanks a lot and congratulations

[@lunnapantt814]

This really helped me to get the idea of Riemann sums .Thanks a lot for saving my time and keep up with your videos.Greeting from Kosovo

[@NoahBraun21]

great video! I'm studying for my Real-Analysis final and this helped explained the basic concepts WAY better than the book did

[@jochem2710]

Thanks, great video! Didn't understand the reasoning going from partitions to the definite integral but now I do, it's actually quite simple.

[@chrisodden]

Glad it helped!

[@myselfdachu6527]

Thank u sir thanks a lot for this it helped me alot in my graduation... U are incredible such an awesome video

[@ezrasteinberg2016]

Nice video, Chris. Now can you give us a video with a proof of the theorem you mention towards the end of this video? You might also want to mention (at least in passing) that a decorated partition is often also called a "tagged partition" and that the size of a partition is also sometimes called the "norm" or the "mesh" of the partition (in case someone looks at another video by someone talking about partitions for Riemann sums).

[@chrisodden]

Hi Ezra. I'm afraid a video covering the "existence theorem" for the limit of Riemann sums is not, at the moment, on my short list - but I hope to post it eventually! Regarding alternate names for the definitions - as usual, you make a great suggestion. When I think of it I try to mention definitions and notation that a viewer might see in another context, but I didn't do it in this case. If I build a companion web page for this video I will certainly include that information.

[@ezrasteinberg2016]

Thanks, Chris. I always look forward to your videos. :-)

[@AbuSayed-er9vs]

Awesome!! Mind Blowing! which I have ever seen to get a very clear idea... lots of thanks...

[@ROBLOXowns]

Great video, you cleared things up for me, thanks!

[@ezrasteinberg2016]

Yes, absolutely first rate explanation, Chris. I look forward to watching ALL of your other videos! :-) btw, do you have a video that shows the proof that ANY sequence of Riemann sums based on decorated (or tagged) partitions has the same limit as any other such sequence of Riemann sums as the norm (or mesh) of the partitions approaches zero provided the function is continuous (or maybe just bounded) on a closed interval?

[@chrisodden]

Thanks, Ezra. Hopefully I can post a few more this summer.

[@absolutelymath3399]

Hey! How did you draw the functions/graphs/? Was it just keynote, seems difficult to have such smooth curves.

[@chrisodden]

Yes, but here are some key points: a) switch the default curve behavior in Keynote to BEZIER! With a bit of experience you can really get fast at creating the curves you need. b) If a graph requires real mathematical accuracy, you can get an assist from desmos: paste a graph into your presentation and then copy the graph with a bezier curve. c) Lately I have simply started to use desmos snapshots directly in a video when the graphical demands are just too high. (See, for example, my recent video on the “Basel problems” in which I plot graphs of Taylor polynomials to compare to the graph of sine.)

[@absolutelymath3399]

@@chrisodden Thank you very much for such a thoughtful and thorough reply. Your videos are really entertaining I will continue to watch.

[@mr.baguettebaguette]

This helped a lot, thank you!

[@mosshotep]

What is the name of the therome you stated and can you provide a rigrous proof if you can.

[@ezrasteinberg2016]

One thing I noticed while listening again to your fine lecture is that you say a left-hand Riemann sum has equal length intervals in the partition and the sampling argument is taken at the left-hand end point of each interval. However, I think the two concepts are distinct, yes? In other words, can't you have a left-hand sum where the partition is not a regular partition (equal subintervals) as well as a regular partition where the sampling arguments are selected arbitrarily within each subinterval? That would mean that left-hand sum, right-hand sum, minimum sum, and maximum sum do not also require a regular partition. Have I got that right? Thanks!

[@chrisodden]

Yes. I have essentially taken the liberty of letting "left hand sum" be shorthand for "Riemann sum using a regular partition with equal subdivisions with left-hand endpoints used for sampling", and the same for right-hand and midpoint sums. This seems to be pretty consistent with common practice, but perhaps only because irregular partitions never really see the light of day in many discussions of Riemann sums. I wish I had thought to make this point explicitly in the video!

[@sumitsana6170]

If we take open interval (a,b) what will be the problem

[@蔺美云]

This is so helpful. Thank you so much!

[@chrisodden]

Glad it was helpful!

[@MaxPicAxe]

Thank you very much for this video!

[@rcontreras9100]

Great Video Chiris! what program do you use to make the slides?

[@chrisodden]

Thanks for the comment, Raffaelle. I create a presentation using Keynote on a Mac, with significant help from LaTeX (via the app LaTeXit, part of the MacTeX package); I have also installed the CMU (Computer Modern Unicode) fonts for compatibility with the math equations. I record the presentation and do any post-production using ScreenFlow.

[@rcontreras9100]

Thanks Chris, I like so much the way you make all those slides effects, are awesome. I would like learn to do it. Greetings.

[@absolutelymath3399]

Nice video! How do you do the animations?

[@chrisodden]

Thanks. It's just a Keynote presentation and I record a screencast on top of it.

[@absolutelymath3399]

Chris Odden oh you do the animations using animations in keynote?

[@chrisodden]

@@absolutelymath3399 Yes. My math typesetting is via LaTeXit, part of the MacTex distribution

[@muhammadfarashp3734]

Great video Helped me a lot Thankyou

[@MathematicsFoundation]

excellent work thank you sir

[@권오익-m3o]

great video!! Thanks.

[@JossinJax]

Superb instruction.

[@sandeepreddy6295]

Awesome!

[@ahmadwachidulkohar2423]

Terima kasih

[@chrisodden]

Sama-sama!

[@navjotsingh2251]

This is awesome, you are the calculus god. I will worship you and start a new calculus religion 😅

[@disciplinenepal5081]

good