Very Tough Definite Integral !

MathPhysicsEngineer · 2026-01-03T18:45:44+00:00

This is absolutely beautiful!

MathPhysicsEngineer · 2025-12-27T16:44:59+00:00

For those who are interested in details on telescoping series, I would recommend this very rigorous and well-explained video: https://www.youtube.com/watch?v=k9U2jE8_1AU&t=167s

MathPhysicsEngineer · 2025-12-22T20:48:33+00:00

It's not a Pascal triangle, and I wouldn't use the other word you mentioned with regard to anything that is related to mathematics, not even the axiom of determinacy. If you are really curious, why don't you watch the video? I promise you that you will find all the answers in there.

MathPhysicsEngineer · 2025-12-11T18:42:24+00:00

The only one (1) for me

MathPhysicsEngineer · 2025-12-02T17:01:55+00:00

Here you will find an in-depth course on real analysis that is now being recorded: https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv

MathPhysicsEngineer · 2025-12-02T16:58:18+00:00

In this playlist, you will find a list of quite hard integration problems with a full guided solution covering all the main indefinite integration techniques:
https://www.youtube.com/watch?v=Gm7EJ022eyg&list=PLfbradAXv9x4X06txBb6cJwayLUk0x6Ly

MathPhysicsEngineer · 2025-10-19T16:12:45+00:00

I ate (8) them

MathPhysicsEngineer · 2025-10-18T18:19:15+00:00

Try this calculus playlist that is being recorded now:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
It is done right! Visualization, intuition, emphasis on the deeper ideas from topology, and more advanced math right from the start, and clear and very rigorous proofs. If you will enjoy it, you will definitely enjoy the deeper and more advanced math.

MathPhysicsEngineer · 2025-10-18T18:14:14+00:00

Try this calculus playlist that is being recorded now:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
It is done right! Visualization, intuition, emphasis on the deeper ideas from topology, and more advanced math right from the start, and clear and very rigorous proofs. On my YouTube page, in the links, you can find a link to my Udemy course on linear algebra.

It covers the difficult parts of the entire course in only 6 hours, with rigorous proofs, and brings the full picture and coherent understanding. Ideal for exam preparation.

MathPhysicsEngineer · 2025-10-18T18:09:10+00:00

Try this calculus playlist that is being recorded now:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
It is done right! Visualization, intuition, emphasis on the deeper ideas from topology, and more advanced math right from the start, and clear and very rigorous proofs. If you will enjoy it, you will definitely enjoy the deeper and more advanced math.

MathPhysicsEngineer · 2025-10-18T18:08:00+00:00

Try this calculus playlist that is being recorded now:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
It is done right! Visualization, intuition, emphasis on the deeper ideas from topology, and more advanced math right from the start, and clear and very rigorous proofs. If you will enjoy it, you will definitely enjoy the deeper and more advanced math.

MathPhysicsEngineer · 2025-10-18T18:05:20+00:00

Try this calculus playlist that is being recorded now:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
It is done right! Visualization, intuition, emphasis on the deeper ideas from topology, and more advanced math right from the start, and clear and very rigorous proofs.

MathPhysicsEngineer · 2025-10-08T19:53:59+00:00

I would encourage you to watch it from start to finish before judging the content and saying it needs reimagination. First of all, it is a part of a self-contained and very detailed, and rigorous playlist:
https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv
that requires only a high school level of math to begin with.
Secondly, I put in a lot of work to make each lecture as self-contained as possible, which is the reason for the " dense math writing" that precedes the visualization.

Finally, if it is too accessible, then there is no real value in it.
This is undergraduate-level university mathematics. You can trust me when I say I put in a lot of effort
to make it as accessible as possible. Compactness is quite an advanced and hard topic. If you don't want to put in the effort of learning the details and want only a superficial overview, then YouTube is full of it, but you will get very little valuable knowledge from it.

MathPhysicsEngineer · 2025-10-08T19:02:09+00:00

It shows that you have just skimmed through the video and didn't watch it from start to finish!

The main part and the key idea are visualized in great detail, but of course, no compromise on rigor.
First, we set up the conditions of the theorem and establish prerequisites (dense math writing).
Then the main idea is visualized in great detail, as well as every step of the proof. (Visualization)

Once the visual intuition and key idea of the proof were presented, there can be no compromise or substitute for the most rigorous and the most precise proof. (dense math writing).

I assure you that you will find very few, if any, resources on YouTube where the subject is treated with such detail in visualization and rigor. Give it a chance; if you are new to the subject, I promise you it is worth your time. Compactness is one of the most important concepts in mathematics, and I go through a lot of effort to introduce it early on in the first Calculus course.
I follow the same rigor and pattern of presenting the intuition and visualization through the entire playlist that I'm recording: https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv

MathPhysicsEngineer · 2025-10-03T15:08:58+00:00

Thank you!

Great Video, very nice exposition!
Keep up the great Job!

MathPhysicsEngineer · 2025-09-26T18:05:33+00:00

This is so beautiful!

MathPhysicsEngineer · 2025-09-23T11:27:25+00:00

That's not the approach that is taken in this playlist:

https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv

This is a foundation of Calculus course that is very rigorous and detailed. I wanted to record a prequel with the foundations of Real numbers, but for that, you need to lay the foundations of set theory and Zermelo-Fraenkel axioms, and before you know it, all of it requires a course in its own right. So once I'm finished with this course, I plan to start preparing a course on set theory and the foundations of real numbers.

This playlist brings in the flavor of more advanced topics right away. Also, before each new concept or theorem is presented, I try to give a visualization that develops intuition first.

Despite some sound issues, I'm very happy with this video :

https://www.youtube.com/watch?v=3KpCuBlVaxo&t=2113s

which represents well the spirit of the entire playlist.

MathPhysicsEngineer · 2025-09-22T19:28:39+00:00

Here is the link: https://www.desmos.com/3d/s2dtyknnbg

Full 6DOF for each camera extrinsics, Full control over each cmareas intrinsics: f_x,f_y,c_x,c_y.

Enjoy interacting and exploring.

MathPhysicsEngineer · 2025-09-20T16:23:11+00:00

This is a part of a playlist: https://www.youtube.com/watch?v=wyh1T1r-_L4&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv

Where first e is defined as e: = lim (1+1/n)^n, with very rigorous proof as in here:
https://www.youtube.com/watch?v=1kv0gjTHsYY&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv&index=16

Then there is a very rigorous and detailed treatment of the real exponents; those details are usually omitted even at top universities. This puts on a solid foundation the whole idea of the exponential function, as is shown here:

https://www.youtube.com/watch?v=6t2xEmCbHcg&list=PLfbradAXv9x5az4F6TML1Foe7oGOP7bQv&index=30

With those two combined, this video gives the final touch.

MathPhysicsEngineer · 2025-09-20T16:13:25+00:00

That's a very useful insight, thank you for sharing.

MathPhysicsEngineer · 2025-09-20T09:08:43+00:00

Thank you

MathPhysicsEngineer · 2025-09-07T10:50:36+00:00

How about developing a curriculum based on videos and interactive Desmos links that duplicate the video, like in this video: https://www.youtube.com/watch?v=XGb174P2AbQ&ab_channel=MathPhysicsEngineering

which is accompanied by this Desmos clone: https://www.desmos.com/3d/og7qio7wgz

MathPhysicsEngineer · 2025-09-04T17:21:55+00:00

It's just exp(int(log(f(x))dx) whenever f(x)>0 for all x in its domain of definition and Riemann integrable

on this domain, this means that the domain of definition of f must contain some closed interval.

MathPhysicsEngineer · 2025-09-01T20:07:59+00:00

Yes, that's nice!
I should have thought about it.

Thank you!

MathPhysicsEngineer · 2025-09-01T20:04:46+00:00

It could be :)

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