Dear Calculus 2 Students, This is why you're learning Taylor Series

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[zachstar]

For anyone that didn't see the most recent video, this channel used to be 'MajorPrep' and the name just recently changed. I'll stop bugging you guys about it after this but I know I'll still get comments from people who don't watch every video on this channel and didn't know about the change. Also if you enjoyed the 'mathematics used to solve crime' video I did a while back you will definitely enjoy the video coming next!

[Mu_Lambda_Theta]

Who even approximates sin(x) as x anymore? That is so yesterday!
*Today, we say 1=cos(x)*
_No, we do not approximate cos(x) as 1, we approximate 1 as cos(x)_

[blissconnect_]

I should be studying calculus 1 right now but might as well see what the future holds for me haha

[justinjustin]

As my calc professor put it some years back: "most equations are rude and hard to work with, but Taylor is great at making them well behaved and easy to work with."

Or as I tend to paraphrase it: "equations can be assholes that are impossible to work with, but Taylor can kick their ass into place so that they're well behaved."

[jsal]

why do 1 feel so uncomfortable with seeing "Calculus 2" instead of "Calculus II"

[RCSmiths]

I feel like you should do a Dear.... for all Calc courses, or just all courses in general like Linear Algebra. That'd help out so much more than you think

[QDWhite]

9:03 I learned the Taylor approximation for the far-field strength of a dipole in my electricity and magnetism class. That was a particularly frustrating day. Our prof had us all attempt it ourselves and we all failed. Then he showed us the Taylor series approximation. When he started striking off terms that "didn't matter" I just about lost it. I left the class thinking "well yeah, anything is easy if you can just call the hard parts insignificant and strike them out. Let's see how he feels about me doing that on the midterm".

As you can tell, I'm so totally over it.

[seangrimes]

Student: what are the purpose of the equations if we can't use them?
Teacher: yes EXACTLY! They have a purpose, they're not just hanging out in reality for no reason 😂

[allensimpson]

Having just finished my Machine Learning Class last semester, I can say with confidence that Taylor Series, while Hell, are far easier for computers to calculate than doing the "normal" method. And when you have to run more than a million calculations of a particular function even a 1% increase in computational speed/efficiency may save HOURS of computing time (given large enough datasets). Even if you aren't in Computer Science, if you have a friend even tangentially interested in AI, being able to lord over them the gift of Taylor Series is going to be worth it for them.

[awabqureshi]

Look at this engineering propaganda smh. Stay in maths; don’t approximate kids

[sharikumar]

We approximate, I didn't mean to round (pi = 3).
Lol, 🤣 🤣 🤣 🤣

[AlbinoJedi]

Thank you. I got a physics undergrad and I've never really understand the Taylor series. The bit at 8:53 where you series expanded the total relativistic energy and turned it into mc^2+.5mv^2 blew my mind.

[lilaismygirl]

This was really helpful. No one has explained the context for using Taylor series which made learning how to do them really hard. Appreciate the in-depth vid!

[sherifffruitfly]

it's funny because newton actually thought of power series as "decimal places for functions". for newton, taylor approximations WERE rounding.

[stephencasper]

I absolutely LOVED Calculus II. Despite not being a mathematics major, Calc II has been my favorite class so far. Having a great professor definitely helped.

[milly]

I love your maths videos because I think it's important to bring the applications of maths closer to those studying it. I wasn't a fan of the subject in school because I simply didn't get why I was being taught something I'd never use. Later on I discovered just how amazing and powerful maths is and by learning about the applications of maths I worked backwards and studied some topics that really got me into it. It's the most interesting field by far but gets such a bad rep in school lol

[Zack-xzph]

I enjoy going back and reviewing the basics, which I was forced to cram during my semesters of calculus. it's also fun to solve problems using C or python once you have a good intuitive understanding

[Scarabola]

You upload this a day before I take my first Cal 2 class in the Spring semester. Stop stalking me!

[okpgamingdk]

Another great video dude! I appreciate the way you teach people the applications of different mathematical topics. It's a great way of motivating people to learn and appreciate math like i do.

[pranaviyer]

Hey Zach I really appreciate you putting out these awesome videos. People like you are what keep my interest in math and physics mainstream. Also, I really enjoyed your skit videos. Those were Fricking hilarious!