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!
How can one not watch all your videos? I have to give you credit for picking interesting topics and explaining it well, and even if I know about things, there is always some new angle or insight as well as nice visualisations.
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)_
Calc 1: Derivatives Calc 2: integrals Calc 3: multivariable Calc 1 and 2 (easier than Calc 1 and 2) Calc 4: Calc 3 but with multiple derivatives and integrals. (Pretty tough but much more fun than it sounds.) There, I just told you the next 2 years of math classes. Lol
@@rijulranjan8514 because you do convergence tests and they're not always straightforward. It's a guess and check kind of thing and it can get super annoying. You'll spend like 10 minutes doing a test to see if an equation converges or not and the test will be inconclusive, so you have to try something else. Will some of the convergence tests you just have to get lucky and do the correct test
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.
Thats so true. I just lost it when i thought the prof and books were messing up eqn. I thought C'mon how do u say that as equal and not mess up later! I lost interest for all E&M, Antennas, microwave.
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."
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
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 😂
@pyropulse they always say that, it doesn't matter who tutors them, as long as it is not the teacher they'll always say "if the teacher taught like you did it's be easier."
@pyropulse because it's harder to have engagment during the lecture. When you tutor, you are having them do actual problems. But during the lecture, it's more about delivering the background knowledge required to do the problems. And it could be a long road from there. When time is limited, some just choose the easy path and just say everything they need and leave the rest to you. The students should proactively take notes and think. But for me lectures don't really work sometimes because when you take notes and think on your own, your mind wanders off and miss the next bit of the lecture. Missing any critical bit of information can make the rest of the lecture incomprehensible.
@pyropulse I've also been an assistant in many courses(albeit electrical engineering and computing science) and all I can say is that I despise your look on students. I've had people who would repeatedly ask simple questions, which I would eventually ask to stop asking simply for they'd slow down my tutorial, but I wouldn't come close to saying "I hated being a student because others asked stupid questions". If you think like that you fail to understand the frustration that comes with studying for so many of your fellow students. My problem with studying always was that there is practically *no* engagement; take for example analysis or calculus. These subjects float somewhere in the realm of extreme abstraction without being applied anywhere until way later(usually masters). Due to the modularity of most studies you'd have a course about them in year 1, then one somewhere in year 2 and sometimes another in year 3, without any logical connection between them. So you'd push yourself through just to have to redo most of it again a while later, instead of making sure everything taught is reinforced by applying it after being taught(and no, jump through the hoop I don't consider applying). I'll also vow for designing semesters in a fashion that would allow particular subjects to be analyzed in depth, before moving on, rather than spreading them out over several years. I think the fact that it isn't is a very large offender in the never ending, as you call it "stupid", questions.
@pyropulse can i ask where do you live? If its USA i found that it is so popular to rely on tutors it almost takes away the responsibility off the students to learn and acts more like a good business model for people in academia around colleges. Mass tutoring isnt that popular in my country.
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.
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.
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!
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
"So although it doesn't sound professional; being good enough is often what we're after." (11:13) I disagree that it's in any way unprofessional to approximate. I'll agree it's not rigoristic in a mathematical and analytical sense, but that's not the point. Without approximations there's a plethora of things we wouldn't have been able to do technologically in today's society. Having an answer that works with 0,x% error is infinitely more professional than not having an answer at all.
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
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.
At around 9:00 , the equation at the top is not an approximation but in fact the same equation as 'm' is not equal to 'm0’. If you plug in the value of 'm' in terms of 'm0', you will get the same equation. The equation which is arrived at the bottom is the approximated equation as it has 'm0' at both places and is only valid for objects not moving at a speed close to light.
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.
Oh my holly forking COW. I've learned Taylor series many times in various classes till the end of my Master's, but JUST NOW got the true intuition on the Taylor Series. Thanks for the crazily awesome video. This is crazy.
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!
As someone teaching differential equations to high school kids, the unit that we have on infinite series always feels weirdly arbitrary to them. This is a great video that really demonstrates a lot of how these things are used in day-to-day calculations. Thank you.
I'm glad you made this video - I enjoy the engineering memes, and I was looking for a reason behind calc 2 because it's definitely more than just learning to integrate more functions. Thank you!
Thank you for doing this As a second year engineering student I had no idea what the point of series was despite getting an A in Calc II, I just thought it was some useless math talk. Now I understand and I have you and this great video to thank for so
10:47 This is why atom appears to be neutral from a distance even though the location of positive charges (nucleus) and negative charges (electrons) are far but not too far from each other.
Thank you! And if you haven't seen them already I've done a few in depth videos on fourier and laplace. Fourier (and some laplace): ua-cam.com/video/3gjJDuCAEQQ/v-deo.html Laplace: ua-cam.com/video/n2y7n6jw5d0/v-deo.html
At 4:17 plugging in y(0)=-1 and x=0 into the differential equation to solve for y’’(0) the equation was written incorrectly as y’’(0) = 0 + y(0) + [y(0)]^2 instead of the correct form y’’(0) = 0 + y(0) -[y(0)^2] but it was evaluated correctly to be -2.
Most springs cease to be useful as springs, once you extend them beyond the linear elastic range. The metal deforms permanently, and the spring doesn't return to its original position. With metal springs, Hooke's law is good enough for the entire reversible elasticity domain, and rarely would you need to know a higher order function to model it. For plastic springs, the stress strain function has curvature in this range, so indeed using Hooke's law is simply a linear approximation.
this video is cool as an algorithmic recommendation because while it is squarely in my interest zone, it is completely outside my understanding and competency so it's just jazz to me
This was so helpful! I wish my calc professor in undergrad could have explained this as well as you did. Thank you for making this video and sharing it!!
You should put keywords in the description so this would pop up when I'm learning about energy, velocity (kinematics), and electrical fields, since that would make learning all that even more interesting and explain how all those formulas are connected. I never made that connection until rewatching this video. This also is intetesting that we are applying the ideas for alternating series in the electric field example.
The applications for the equations are left in youtube for us to browse i wish i had math a teacher who could teach me math like this You are doing a hell of a job brother keep going.........😍
Yeah e^x just happens to have an infinite radius of convergence, maybe should've been more specific about that but no it's not always a perfect approximation.
NICE! Some numerical methods, like Runge-Kutta, are derived from some terms of a Taylor series, also, some differential equations, like the heat conduction and the famous Navier-Stokes, are derived from some terms of a Taylor series.
I appreciated watching this video very much - in some sense, I gather mathematic is a bit like art. There is a sort of piece where its about intuition, and you make those aproximation and it works in certain cases.
God damn it, i took Calculus and Linear Algebra 3 years ago, and i already forgot so much of the concepts. I hate that we continuously forget stuff, even some of the stuff we understand, and we have to practice it frequently in order to remember it long term. Now, i'm here, re-reviewing my Calc and Linear Algebra, the human brain, as complex and amazing as it is, sucks at recalling things that we already learned.
Right... Babies never ,"learn English" in order to speak it. All American Babies just yell, "mERica!" as they slide out of the birth canal. Afterwords they immediately realize that America is so great that you don't have to learn any other languages in order to thrive. #DontHateThePlayerHateTheGame
Thank You so much. Please help by answering this question, as average students how do we visualize day-to-day topics of our stream, and find their practical use and how are they applied in the complete process. Just like a regular CS student knows how to implement all the data structures but the actual code used in production is way different than those taught or written in classrooms, how to bridge that gap, and get the actual reality/purpose of the concept.
A lot of content electrodynamics course as a physics major dealt with approximations just like that last example. Everything in STEM, minus pure math is approximation.
if you use taylor series to solve for PDE's, you are going to either make a super computationally unstable/inefficient algorithm or one that just doesn't work (due to discontinuous boundary conditions or such). The REAL reason you learn Taylor series is so that you can kinda learn a bit of numerical analysis, and THEN you learn the real shit known as "Fourier Series". Fourier Series can be used to solve anything if you have the right spectral resolution and sample rate.
A mathematician and an engineer were both chaparones at a middle school dance. There was a line of boys, and a line of girls, who started 16 feet apart, and were very shy of one another. Every minute, they halved the distance to each other. From 16 ft to 8 ft, then 8 ft to 4 ft, and so on. The mathematician remarked, "they will never make to each other." The engineer replied, "yeah, but in a few minutes, they will be close enough for all practical purposes".
Not only is it weird seeing calculous 2 instead of II we used to call it the Mclovin series intead of Maclaurin just for the memes but now it's stuck 😂
Very nice video and explain👍 with idea for choice this topic . There topic now no one explain or not explain by simple (why we using and where are come from ?) way in any video before which it "Differintion Equation with Orders" (ODE) . Thank you Zack ... keep going .
This is probably as good a single-use motivation as any. But the viewer should be aware that the Taylor series is at the heart of analytic functions and complex analysis. Those subjects have many profound consequences aside from the ability to approximate. A more accurate title would be: This is ONE REASON you are learning Taylor series.
I don't know how but i was unsubscribed after the channel name change. Good thing that the video came to the recommended section and i noticed and i subbed again.
At 10:01 I smell something fishy. It appears you did (x+a)^2 = (x^2+a^2)=x^2(1+(a/x)^2)=(x^2)(1+a/x)^2 which isn't true. Did you do this intentionally as an approximation for small values of a?
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!
Second like.
@VeryEvilPettingZoo -- 3 = pi = e.
Oksy, i came to ask what happened to MajorProp that his voice've transferred to a new channel. I see now
How can one not watch all your videos? I have to give you credit for picking interesting topics and explaining it well, and even if I know about things, there is always some new angle or insight as well as nice visualisations.
I liked the old name better, and I admit I was quite confused because I didn't remember subscribing to a channel named Zach Star :]
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)_
@@Zack-xz1ph You probably mean -(x^2)/2
I approximate sin x to be tan x
i mean if you do that
1+sin^2(x)=cos^2(x)
which is cool
We dont do that here
As long as x is really small
I should be studying calculus 1 right now but might as well see what the future holds for me haha
Don't mind you gonna fail
Calc 2 is a whole different ballpark lol
Calc 1: Derivatives
Calc 2: integrals
Calc 3: multivariable Calc 1 and 2 (easier than Calc 1 and 2)
Calc 4: Calc 3 but with multiple derivatives and integrals. (Pretty tough but much more fun than it sounds.)
There, I just told you the next 2 years of math classes. Lol
Slim Jim why is Calc 2 considered so hard? I'm also in Calc 1 and it seems like everybody at my school dreads it
@@rijulranjan8514 because you do convergence tests and they're not always straightforward. It's a guess and check kind of thing and it can get super annoying. You'll spend like 10 minutes doing a test to see if an equation converges or not and the test will be inconclusive, so you have to try something else. Will some of the convergence tests you just have to get lucky and do the correct test
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.
mellow I’m taking e&m this semester, if I remember, ilyk
Thats so true. I just lost it when i thought the prof and books were messing up eqn. I thought C'mon how do u say that as equal and not mess up later!
I lost interest for all E&M, Antennas, microwave.
Me too... But I still gotta face it
@@plentygolden Yep. E&M and Stat Mech. Did a number on my GPA back in the day.
Ok, I'm two years late but whatever.
When they say "far-field" they always mean in an asymptotic sense.
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."
@pyropulse This one is going in my cringe compilation
im surprised marvel never made a comic about the taylor hero!
@@pewpew9711😂😂😂😂
why do 1 feel so uncomfortable with seeing "Calculus 2" instead of "Calculus II"
calculus two
Seems like you're fine with writing "why do i" instead of "Why do I" so I think you'll get over it
2(Calculus)
Calculus 1+1
calculus 2rd edition
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
"Linear Algebra" ~ Gilbert Strang MIT
ua-cam.com/video/7UJ4CFRGd-U/v-deo.html
"Linear Algebra" ~ 3Blue1Brown
ua-cam.com/video/fNk_zzaMoSs/v-deo.html
@@douglasstrother6584 this is obviously not the same format
I can vouch for 3B1B teachings
"Introduction to Linear Algebra" ~ Gilbert Strang
math.mit.edu/~gs/linearalgebra/
Look at this engineering propaganda smh. Stay in maths; don’t approximate kids
Lmao
Pure mathmatics do not approximate rather abstract.
Clearly has not studies PNT as the prime counting function is an approximation.
Mathematicians hate engineers because they take math and apply it for something with practical value.
@@Cyberspine An applied mathematician enters the chat.
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 😂
@pyropulse they always say that, it doesn't matter who tutors them, as long as it is not the teacher they'll always say "if the teacher taught like you did it's be easier."
@pyropulse because it's harder to have engagment during the lecture. When you tutor, you are having them do actual problems. But during the lecture, it's more about delivering the background knowledge required to do the problems. And it could be a long road from there. When time is limited, some just choose the easy path and just say everything they need and leave the rest to you. The students should proactively take notes and think. But for me lectures don't really work sometimes because when you take notes and think on your own, your mind wanders off and miss the next bit of the lecture. Missing any critical bit of information can make the rest of the lecture incomprehensible.
@pyropulse I've also been an assistant in many courses(albeit electrical engineering and computing science) and all I can say is that I despise your look on students. I've had people who would repeatedly ask simple questions, which I would eventually ask to stop asking simply for they'd slow down my tutorial, but I wouldn't come close to saying "I hated being a student because others asked stupid questions". If you think like that you fail to understand the frustration that comes with studying for so many of your fellow students.
My problem with studying always was that there is practically *no* engagement; take for example analysis or calculus. These subjects float somewhere in the realm of extreme abstraction without being applied anywhere until way later(usually masters). Due to the modularity of most studies you'd have a course about them in year 1, then one somewhere in year 2 and sometimes another in year 3, without any logical connection between them. So you'd push yourself through just to have to redo most of it again a while later, instead of making sure everything taught is reinforced by applying it after being taught(and no, jump through the hoop I don't consider applying). I'll also vow for designing semesters in a fashion that would allow particular subjects to be analyzed in depth, before moving on, rather than spreading them out over several years. I think the fact that it isn't is a very large offender in the never ending, as you call it "stupid", questions.
@pyropulse can i ask where do you live? If its USA i found that it is so popular to rely on tutors it almost takes away the responsibility off the students to learn and acts more like a good business model for people in academia around colleges. Mass tutoring isnt that popular in my country.
@@howardlam6181 true. Never learned anything from school, but when I read the books on my own I understand it perfectly.
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.
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.
Omg this motivated me
i just started to learn taylor series for computer science
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!
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
"So although it doesn't sound professional; being good enough is often what we're after." (11:13)
I disagree that it's in any way unprofessional to approximate. I'll agree it's not rigoristic in a mathematical and analytical sense, but that's not the point. Without approximations there's a plethora of things we wouldn't have been able to do technologically in today's society. Having an answer that works with 0,x% error is infinitely more professional than not having an answer at all.
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
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.
Yeah it was a interesting class.
You upload this a day before I take my first Cal 2 class in the Spring semester. Stop stalking me!
Lol same
At around 9:00 , the equation at the top is not an approximation but in fact the same equation as 'm' is not equal to 'm0’. If you plug in the value of 'm' in terms of 'm0', you will get the same equation. The equation which is arrived at the bottom is the approximated equation as it has 'm0' at both places and is only valid for objects not moving at a speed close to light.
This is amazing... My teacher always says that he loves the Taylor series.. now I know partly why.
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.
We approximate, I didn't mean to round (pi = 3).
Lol, 🤣 🤣 🤣 🤣
=e=(g-1)^.5
355/113
Absolutely hilarious
Guys let it be π.
355/133 seems a bit irrational...
Sounds like an engineering class
Oh my holly forking COW. I've learned Taylor series many times in various classes till the end of my Master's, but JUST NOW got the true intuition on the Taylor Series. Thanks for the crazily awesome video. This is crazy.
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!
5:06 "perfect approximation" sounds weird
As someone teaching differential equations to high school kids, the unit that we have on infinite series always feels weirdly arbitrary to them. This is a great video that really demonstrates a lot of how these things are used in day-to-day calculations. Thank you.
I'm glad you made this video - I enjoy the engineering memes, and I was looking for a reason behind calc 2 because it's definitely more than just learning to integrate more functions. Thank you!
Thank you for doing this
As a second year engineering student I had no idea what the point of series was despite getting an A in Calc II, I just thought it was some useless math talk. Now I understand and I have you and this great video to thank for so
10:47 This is why atom appears to be neutral from a distance even though the location of positive charges (nucleus) and negative charges (electrons) are far but not too far from each other.
Wow. Someone finally speaking mathematics. Very much satisfied. Great job expecting more regarding Laplace and Fourier transform
Thank you! And if you haven't seen them already I've done a few in depth videos on fourier and laplace.
Fourier (and some laplace): ua-cam.com/video/3gjJDuCAEQQ/v-deo.html
Laplace: ua-cam.com/video/n2y7n6jw5d0/v-deo.html
At 4:17 plugging in y(0)=-1 and x=0 into the differential equation to solve for y’’(0) the equation was written incorrectly as
y’’(0) = 0 + y(0) + [y(0)]^2 instead of the correct form y’’(0) = 0 + y(0) -[y(0)^2] but it was evaluated correctly to be -2.
Great stuff. It's frustrating that the motivation is so often never mentioned.
I needed this video 3 years ago.
I love this, I watched this while talking calc 1 a year ago and today was my last day of calc 2!!! I understand this so much now 😍
Hooke's law of spring force is also a linear approximation of real spring force.
Most springs cease to be useful as springs, once you extend them beyond the linear elastic range. The metal deforms permanently, and the spring doesn't return to its original position. With metal springs, Hooke's law is good enough for the entire reversible elasticity domain, and rarely would you need to know a higher order function to model it.
For plastic springs, the stress strain function has curvature in this range, so indeed using Hooke's law is simply a linear approximation.
this video is cool as an algorithmic recommendation because while it is squarely in my interest zone, it is completely outside my understanding and competency so it's just jazz to me
What do you mean "doesn't sound professional"? "Good enough" is essentially the definition of "professional" 🤣
Thanks!
This was so helpful! I wish my calc professor in undergrad could have explained this as well as you did. Thank you for making this video and sharing it!!
I like the Equioscillation theorem from Tschebyschow a bit more then the Taylor Approximation.
You should put keywords in the description so this would pop up when I'm learning about energy, velocity (kinematics), and electrical fields, since that would make learning all that even more interesting and explain how all those formulas are connected. I never made that connection until rewatching this video. This also is intetesting that we are applying the ideas for alternating series in the electric field example.
I feel so interesting when you say about it's applications but in classes solving problems by hands makes me de motivate
Thanks for this video. I find it really helpful to know what motivates the techniques we learn.
Hey hey! Teaching series next month - I'm going to play this video for them then. Thanks!
We talked about Taylor Series in my Numerical Methods class today. I’m glad I found this
Mom: are you studying?
Me:
Thanks for the informative overview, nice. I like and appreciate your videos
Without Taylor Series, we'll have to go to "Plan B": philosopher, musician, poet, bar bouncer.
What is a bar bouncer?
Bouncer: www.urbandictionary.com/define.php?term=bouncer
The applications for the equations are left in youtube for us to browse i wish i had math a teacher who could teach me math like this
You are doing a hell of a job brother keep going.........😍
I make math content on my channel
Thank you for posting this AFTER I take calc 2 LMFAO
Спасибо!
Hey great video. My physics professor was going through a derivation and used these and I was so lost. Now it makes loads of sense, thanks.
2:41 WAIT that only works with some functions there are a bunch of them that aren't equal to it's Taylor series.
@pyropulse precisely
@pyropulse yes
Yeah e^x just happens to have an infinite radius of convergence, maybe should've been more specific about that but no it's not always a perfect approximation.
e=mc^2 itself is an approximation based on the first term of a Taylor series.
Thanks, perfect motivation to study for the final
Wow, and I thought I had forgotten everything I learned in Calculus
Please make videos on detailed understanding about various techniques on solving differential equations numerically
NICE!
Some numerical methods, like Runge-Kutta, are derived from some terms of a Taylor series, also, some differential equations, like the heat conduction and the famous Navier-Stokes, are derived from some terms of a Taylor series.
I appreciated watching this video very much - in some sense, I gather mathematic is a bit like art. There is a sort of piece where its about intuition, and you make those aproximation and it works in certain cases.
Well done! But, when I solve the world's energy crisis, should I mention Zach Star or Major Prep in my Nobel acceptance speech??
Students often ask for the applications of the topic we're learning, not realizing many of the concepts we know didnt have any applications at first.
We do the Taylor expansion because, at equilibrium, it is quadratic…and that is exactly solvable as simple harmonic oscillators
Define engineering in two words
Me: 1:07
Love this! Thank you very much :)
God damn it, i took Calculus and Linear Algebra 3 years ago, and i already forgot so much of the concepts. I hate that we continuously forget stuff, even some of the stuff we understand, and we have to practice it frequently in order to remember it long term.
Now, i'm here, re-reviewing my Calc and Linear Algebra, the human brain, as complex and amazing as it is, sucks at recalling things that we already learned.
fascinating! Didn't know maclaurin series is this useful.Thnx for letting us know. :)
Crazy that I watched this video in class today knowing that the other channel exists
Calculus 2?!?
i ALrEaDy hAd ThIs iN eLemEnTeRy ScHoOL!!
Right... Babies never ,"learn English" in order to speak it. All American Babies just yell, "mERica!" as they slide out of the birth canal. Afterwords they immediately realize that America is so great that you don't have to learn any other languages in order to thrive. #DontHateThePlayerHateTheGame
Congrats on your videos. I wish I had a resource like that 28 years ago, when I was studying calculus.
Love your work pal. I am 57 yrs old and trying my best to understand math and your work is very helpful 😊👍
I didn’t understand. Maybe because I still lack the prerequisites of this topic but great video though. I understood the essence of this taylor series
As an engineering student, I have to say your videos are very helpful and much easier to understand than 3b1b 😁
Watching videos like these makes me wish I actually tried harder in high school calculus
Thank You so much.
Please help by answering this question, as average students how do we visualize day-to-day topics of our stream, and find their practical use and how are they applied in the complete process.
Just like a regular CS student knows how to implement all the data structures but the actual code used in production is way different than those taught or written in classrooms, how to bridge that gap, and get the actual reality/purpose of the concept.
Taylor approximations can solve problems and simplify some math formulas (eg Taylor series can solve complicated limits better than l’hopitals)
e^x vs e^x (Taylor's Version)
taylor swift never learns that e^x.
A lot of content electrodynamics course as a physics major dealt with approximations just like that last example. Everything in STEM, minus pure math is approximation.
Well Thanks For Great Introduction For Series 😘
Gonna Learn Them Next Year 🔥
>the first e^x example
8 years of calculus [40 years ago] and no-one ever told me WHY!
thanks, Zach.
same here , it was just trying to memorize meaningless junk , now 5 yr olds get a better understanding
I studied Maclaurin Series recently in Alevel Further Maths. It was good to know the reason for it 😍😍😍
Trinidad?
@@Chrisratata sorry I dont understand what you mean
"love on a real train" by tangerine dream on the background, huh, nice
Doing Math 1 for natural scientists atm, and already doing taylor series
THANK YOU
1:03 You Filthy Engineers
You mean 1:10
113355. now separate: 113 355. flip and divide. 355/113 ≈ π
if you use taylor series to solve for PDE's, you are going to either make a super computationally unstable/inefficient algorithm or one that just doesn't work (due to discontinuous boundary conditions or such). The REAL reason you learn Taylor series is so that you can kinda learn a bit of numerical analysis, and THEN you learn the real shit known as "Fourier Series". Fourier Series can be used to solve anything if you have the right spectral resolution and sample rate.
4:07 why is there a plus sign on the last term?
Typo, should’ve been a minus.
silence fool! do not question the sacred math scriptures!
What is a difference between a mathematician and engineer? Topology and approximation
A mathematician and an engineer were both chaparones at a middle school dance. There was a line of boys, and a line of girls, who started 16 feet apart, and were very shy of one another. Every minute, they halved the distance to each other. From 16 ft to 8 ft, then 8 ft to 4 ft, and so on.
The mathematician remarked, "they will never make to each other."
The engineer replied, "yeah, but in a few minutes, they will be close enough for all practical purposes".
I am an enginering student and I confirm we have studied topology 😀
I remember the estimation unit in 6th grade math. I always estimated wrong, I guess.
Not only is it weird seeing calculous 2 instead of II we used to call it the Mclovin series intead of Maclaurin just for the memes but now it's stuck 😂
1=v^2 /c^2 and c is speed of light
I think It's time to get re admission in UG my university
Very nice video and explain👍 with idea for choice this topic .
There topic now no one explain or not explain by simple (why we using and where are come from ?) way in any video before which it "Differintion Equation with Orders" (ODE) .
Thank you Zack ... keep going .
zach star himself is a genius.
Could you do a video on quantum computing and what majors/minors needed in your undergrad to get into the field?
Awesome channel, aewsome content, thank you!
This is probably as good a single-use motivation as any. But the viewer should be aware that the Taylor series is at the heart of analytic functions and complex analysis. Those subjects have many profound consequences aside from the ability to approximate. A more accurate title would be: This is ONE REASON you are learning Taylor series.
0:29 black car takes the exit last second
I always round up pi to 10 so it cancels g out.
I don't know how but i was unsubscribed after the channel name change. Good thing that the video came to the recommended section and i noticed and i subbed again.
Well dang u could have told me this before I'd completed calc 2 in December
@pyropulse oh dude I was joking lol, I understood the application I always do that for my math classes cuz it's interesting
@pyropulse eh it's alright I couldn't sense certain jokes sometimes as well
Thank you
At 10:01 I smell something fishy. It appears you did (x+a)^2 = (x^2+a^2)=x^2(1+(a/x)^2)=(x^2)(1+a/x)^2 which isn't true. Did you do this intentionally as an approximation for small values of a?
No that part wasn't an approximation, it's exact. It simplifies as shown below
(x+a)^2 = [x(1+a/x)]^2 = x^2(1+a/x)^2