Real Analysis 44 | Higher Derivatives

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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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#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives
#Studying
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)
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[@azizmdj7583]

Thank you so much sir

[@brightsideofmaths]

Most welcome

[@JojiThomas7431]

Good video

[@lueelee6063]

Is 0 in the natural numbers for this series? Why not consider C^0(I)?

[@brightsideofmaths]

For me, 0 is not a natural number. C^0(I) would then just be C(I) but zero-times differentiable sounds strange ;)

[@lueelee6063]

@@brightsideofmaths Ah i understand. To me C^0 is just the general space of continuous function including things like absolute value function

[@brightsideofmaths]

@@lueelee6063 Yeah, for sure. That should be understandable. However, I use just C for these functions :)

[@angelmendez-rivera351]

@@brightsideofmaths The concept of 0-times continuously differentiable functions is useful to have, though, in particular when discussing Taylor's theorem and other theorems in analysis.

[@angelmendez-rivera351]

@@brightsideofmaths Also, I would argue that using the notation C(I) for continuous functions rather than continuously differentiable functions is clunky, confusing, and an inconsistent usage of notation.

[@adityaekbote8498]

Nice