Calculus 3: Arc Length and Curvature (Video #9) | Math with Professor V

Definition of arc length for curves in space, finding an arc length parameterization for a vector function; curvature and the multiple formulas to compute it; principal normal vector, binormal vector, and the TNB frame; osculating circle in terms of curvature. #curvature #calculus3 #mathtvwithprofessorv #youtubemath #mathprofessor #calculus #mathvideos #TNBframe #unitnormal #unittangent #binormal
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[@mathwithprofessorv]

Note: at 53:04 forgot to write “prime” in the denominator, it should be |T’|.

[@georgethompson4599]

Very good explanations. Thanks!

[@mathwithprofessorv]

You are welcome!

[@gigilifehere]

can someone explain to me why for the example at 8:58 find the arc length for the circle, how we get that x = kcost , y = ksint? thank you!

[@aracal2047]

Thanks a lot

[@raulcervantesramirez3643]

hello, do you have any resources we can use to practice more? like on patreon ?

[@mathwithprofessorv]

I have worksheets, practice exams, etc I put on Patreon-I just haven’t uploaded much Calc 3 yet but I can soon. Email me so we can chat! [e-mail]

[@valeriereid2337]

I am a little lost at 18:18 how we got 5/2 sin^2. Can someone help with a little explanation? Thanks

[@chamnil8666]

here ,we can take 5 out of the integral sign
then do a u substitution(since we have u as a variable already),take 'w' as a variable.
so we can do w = sinu so derivative of w = cosu du
dw = cosu du
now replace sinu with w and cosu du with dw
now take antiderivative of w
it is w^2/2
since we already have 5 outside,
5/2 w^2
now replace w with sinu
so we get 5/2sinu^2

[@valeriereid2337]

@@chamnil8666 Thanks

[@madhurajoshi6963]

34:54

[@AustinGerrard]

❤❤

[@FreeShaima]

The numbers and the math in this section are so ugly and I keep making mistakes 😭
But thank you professor for the good explanation!

[@mathwithprofessorv]

Ugh I know...it makes it hard to focus on the content sometimes, but in Calc 3 you gotta learn to power through! You can do it!

[@FreeShaima]

@@mathwithprofessorv Thank you professor 😇

[@champsinger]

Why do I feel like calc 3 is harder than calc 2 lol

[@oliviadillon9253]

NEVER THAT calc 2 took me out fr