Einstein Summation Convention: an Introduction

In this video, I introduce Einstein notation (or Einstein Summation Convention), one of the most important topics in Tensor Calculus. Einstein notation is a way of expressing sums in short-form; repeated indices are used to denote the index that is summed over.

I describe the 4 major rules of Einstein notation, as well as the definitions of free and dummy indices. I also discuss some important information related to these major rules.

Questions/requests? Let me know in the comments!

Special thanks to my Patrons for supporting me at the $5 level or higher:
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[delta]

"Family show" oof can't wait to sit down and watch some tensor calculus with the fam later tonight.

[johnr]

I love you man
Sincerely,
An engineering Student

[jacobvandijk]

Mnemonic: a DUMMY INDEX really is a SUMMY INDEX !!!

[drunkoncheese]

That handwriting is 🔥! Thanks for the video!

[vijaysinghchauhan]

No words would be sufficient to express my gratitude for this amazing playlist.
Everything is to the point without missing any details.

[XanderGouws]

Spiderman + Elsa vs Tensor Calculus [gone wrong!!]

[ChaineYTXF]

Simply superb. I'm about to delve into the massive (pun intended) book "gravitation" and needed a quick recap of enstein's notation and tensor calculus. So far, a must-watch, your videos are perfect.
Nice handwriting, too
From France, big thanks

[VaradMahashabde]

Me : * tries to understand Einstein notation *
Also me : but why would you torture yourself like that?

[acebdf]

Thank you for explaining the notation convention! I got really confused with other videos on this topic because nobody bothered to take a second and explain this!

[Gismho]

Excellent video. Highly instructive and very well presented. Looking forward to sequels. Thank you.

[jitapriyadas]

Great introduction to tensor calculus, looking forward to the next lectures in this series :)

[drewansan]

Thank you very much for this series of lectures. Very succinct and clear to understand. Looking forward to the next lecture.

[ethannguyen]

Genie before Einstein notation: “There are three rules”
Genie after Einstein notation: “There are four rules”

[ameerbux]

thank you so much for the logical, simple explanations! Mahn ive been so confused over this, now i understand. Giving you a like for every video from now on. On the side, i appreciate the writing being at the same speed which you speak at, thats cool af.

[sumitkumarsahoo]

you are writing super fast, a big salute for your explanation

[tushermyth]

Your way of explaining is quite structured. I like that! Thanks!

[sygon]

Sir, thank you so much for this Video. I dont understand why university lectures don't sum up the material like that and talk endlessly about irrelevant bs

[adventurebecca]

This was exactly the explanation I was looking for!

[aarondrossart]

Explained 3 lectures in 9 minutes. Thanks!

[isaiahmillsterry]

Phenomenal video. Cleared up my questions before I even had them lol