Real Analysis 28 | Epsilon-Delta Definition

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

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00:00 Intro
00:40 Epsilon-Delta criterion
04:32 Proof
08:28 Credits

#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[lesetjamojapelo]

This guy might just single handedly carry me through real analysis

[statweb]

this guy is great! highest quality, math content. Keep up the amazing job!

[samehnour]

Please do not stop with these series, you helped me through LA and now in Analysis.. you are single handedly leading me toward my cs degree .. Thank you

[sharonnuri]

Could not visualize when I read this theorem in my textbook. Thanks a lot for the clear explanation

[philologusopinus]

Ive looked through 10 videos now and yours is the first that properly visualizes what delta and epsilon mean. Thx man

[odxdirk]

finding you has made my homework grade go from D to A- no joke, thank you king

[sanelprtenjaca]

We used this not as a theorem, but rather as a definition of continuous function. Interesting.

[minamishi]

So this is my informal paraphrase of the delta epsilon definition: "if the limit L exists at x = A, no matter how small epsilon is, there will exist a set of x values, which satisfies the condition |x - A| ≤ delta (where delta is a value we have to find but we know it exists) so that |f(x) - L| ≤ epsilon"....is that correct or close to correct?

[dhananjaytudu]

Really great! Very interesting proof and short proof, wonderful 😍

[shibshankardey]

Could you plz upload a video on the uniform and absolute continuity and their difference along with continuity? I am struggling to see any video on them. It will be helpful to many I believe

[jronirons]

Why exclude x_0 with regards to the sequence ? Isn’t x_0 required to be in the domain of said function.

[lwuquh]

Why do you pick delta to be 1/n. That is not exhaustive of real > 0?

[jhonnattanleonardovelasque]

Hey guys! Greetings froms Colombia. I'm fan of your channel. I love all videos. Thanks a lot for this invaluable knowledge. I'll know what tools do you use to write and record the videos?

[demaskoh]

Referring to the last example in Video 27: is there continuity for irrational numbers by using the epsilon-delta definition? I read in Sutherland (2009) that a function as such would be discontinuous at Q but continuous at R\Q. 🤔

[desperatewanderer]

why can't my math teacher be this good

[snipergod]

has anyone ever told you, you sound an awful lot like PewDiePie?