I want to say this to you-- your channel is a goldmine. You make concise videos on essential topics of a subject. This saves so much time for those who want to learn the essentials without having to watch hours long lectures. I am so so grateful for this service of yours. Request: Please make series on Linear Algebra (with advanced topics), and Multivariable Analysis (with manifold stuff, and classical theorems of vector calculus). That will be so awesome! Thank you again.
What is the justification for the step “there exists mu such that…” around @5:30? It’s intuitively clear, but at the moment I can’t think of which specific theorem allows us to make that step.
I can't understand the part where you transform [ int (x) to (x + h) of f(t) dt ] into [ f(x hat) times h ] with the mean value theorem of integration. Shouldn't it be [ f(t hat) times h ] ? It's at 8:05.
I've got queries in the proof of the second fundamental theorem of calculus: 1) Fo(a) = 0 implies the theorem holds for Fo because on the LHS the integral is indeed just 0 and on the RHS we have F(a) - F(a) = 0 = LHS right? 2) In the last step Fo(b) - Fo(a) = integral from a to b f(t) dt because we already proved that the theorem works for Fo? I got quite confused here because we proved it works purely by using Fo(a) = 0 and nothing about Fo(b) :( 3) Lastly, how can we relate area to slope through FTC I can't seem to draw any conlcusion 😢
I think giving an example of what the fundamental theorem of calculus doesn't prove would be beneficial here. I'm thinking about the integral of the Normal density.
![Real Analysis 62 | Integral Test for Series [dark version]](http://i.ytimg.com/vi/rbPhKSd5mA8/mqdefault.jpg)
I want to say this to you-- your channel is a goldmine. You make concise videos on essential topics of a subject. This saves so much time for those who want to learn the essentials without having to watch hours long lectures. I am so so grateful for this service of yours. Request: Please make series on Linear Algebra (with advanced topics), and Multivariable Analysis (with manifold stuff, and classical theorems of vector calculus). That will be so awesome! Thank you again.
Thank you very much!
Linear Algebra and multivarible calculus are in production, see here: tbsom.de/s/la
Advance topics will come :)
Ich mache grade meine Promotion in Physik und bin längst mit allen Mathematik Kursen durch, aber die Videos machen trotzdem immer Spaß :D
What is the justification for the step “there exists mu such that…” around @5:30? It’s intuitively clear, but at the moment I can’t think of which specific theorem allows us to make that step.
Just define mu by the quotient of both integrals. That's all :)
I can't understand the part where you transform [ int (x) to (x + h) of f(t) dt ] into [ f(x hat) times h ] with the mean value theorem of integration. Shouldn't it be [ f(t hat) times h ] ? It's at 8:05.
It's the means value theorem. How you call the intermediate point does not matter. It's just a name.
i am studying in iitb, and my teacher failed to teach a topic, that could be taught so easily
I've got queries in the proof of the second fundamental theorem of calculus:
1) Fo(a) = 0 implies the theorem holds for Fo because on the LHS the integral is indeed just 0 and on the RHS we have F(a) - F(a) = 0 = LHS right?
2) In the last step Fo(b) - Fo(a) = integral from a to b f(t) dt because we already proved that the theorem works for Fo? I got quite confused here because we proved it works purely by using Fo(a) = 0 and nothing about Fo(b) :(
3) Lastly, how can we relate area to slope through FTC I can't seem to draw any conlcusion 😢
Such long questions are best discussed in my community forum.
another awesome video :D
Thanks again!
I think giving an example of what the fundamental theorem of calculus doesn't prove would be beneficial here. I'm thinking about the integral of the Normal density.
This video is about the proof of the theorem :)
Ander great video
Thanks!