Descrizione
In this episode of the Taylor Series, we discover the entry point to Calculus. We found that while you cannot divide a non-zero number by zero due to contradictions with other fundamental axioms of math, the expression 0/0 does NOT have those contradictions. While we can’t assign a value to 0/0 if we come across it in an analysis, we might be able to work around it! That is the thrust of this video, and in it we discover the ideas of limits, average and instantaneous rate of change.
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Hey! It’s been a bit. I’m still out here with stuff planned! I have been hesitant to pontificate on what my plans for the future are, as life seems to be many curve balls in a row. Still, I have learned a lot over the past year with regards to Blender, and you can even see a short clip I made for this video in Blender. The idea for this video was teased at the end of the one I did prior -- the one that goes over whether or not you can divide by zero -- and when I saw the competition that 3Blue1Brown was hosting, I couldn’t resist making it.
As a side note, I seem to refine my process pretty regularly. This video actually represents a pretty big push forward for my process, in particular, incorporating Blender and Desmos into my videos more frequently. Suffice it to say that it adds layers (pun totally intended for all those out there who edit videos) of complexity, but I think I’ve got something that can handle it. I might post a vlog thing about it at some point, because… it’s actually pretty interesting!
Anyway, transitioning into sounding like an email, I hope you’ve all been well, and I look forward to seeing you in the next video. :)
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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Patreon:https://www.patreon.com/TaylorSeries
Facebook:https://www.facebook.com/TheTaylorSeries
Twitter:@TheTaylorSeries
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Music Credits (from AudioBlocks):Intro music:
Thinking by Patrick Smith
Main background music: Island Fun by Neil Cross
Silly Guitar Music: Funky Samba by Neil Cross
Outro music: Midnight City Lights by Neil Cross
Upbeat music: No More No less by Mikael Manvelyan
Funky upbeat music: isberg by Mikael Manvelyan
Sad Piano Music: Beautiful Piano by Jason Donnelly
Icon Credits: Event Horizon Telescope collaboration et al., an AMAZING picture of a black hole.
Software Credits: Desmos! Desmos is amazing. Go check it out: www.desmos.com
I also used myriad Adobe Suite products (After Effects, Photoshop, Premiere Pro, etc.), Blender, and OBS.
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00:00 - Intro and Motivation
01:35 - Time in Functions
02:08 - Rate of Change of a Line
03:35 - Average Rate of Change
04:39 - Instantaneous Rate of Change
05:52 - Graphically Exploring Average vs. Instantaneous RoC
06:38 - Settup up Calculation for Instantaneous RoC
08:23 - Oh noes, not 0/0
08:53 - Using Limits to find Instantaneous RoC
10:28 - The Exact Instantaneous RoC at t = 1
11:14 - Further Explorations - Delta-Epsilon Proof
11:49 - Further Explorations - The Derivative
12:27 - Further Explorations - The Ethos
13:42 - Wrapup and Outro