Adam Shafer. Lol, you’re not smart. I’m done with math and I finished it in 6th grade. I’m current teaching my 5th grade brother. Anyone any age can finish calculus by simply indulging yourself in the mindset of perceiving ideas as easy. That’s how I finished multi variable in a month. Lol, multiple integrals and partial derivatives were just tiny pieces of CAKE!!! I also finished AP physics and AP chemistry and I’m looking forward to finishing more AP classes. I don’t know if it’s just my own idiosyncratic way of learning though, my siblings just don’t seem to understand my way of learning and memorizing. Anyways, you were just talking to an IMO (International Mathematics Olympiad) participant and a 3X Mathcounts finalist who finished all of calculus within months so...BYE. By the way, I’m not flexing.
I'm the kind of guy who relies heavily on step by step examples and equations while doing my work. The video was really helpful, I hope you make many more like this. Thanks a lot!
you save engineering students lol. I have time to hit the gym and pursue my passion for bodybuilding because I can watch your videos instead of reading through the textbook for hours lol. Gotta love UA-cam. Obviously youtube cant always grasp the level of difficulty of practice problems they give you engineering cause they make it alot harder, its still extremely helpful to understand the concept as quickly as possible instead of using a textbook lmaoo, then from there you can just practice harder problems of the same concept.
Oh thank god. I've been studying for my calculus final (which is tomorrow) and Newton's Method is the only thing I've been having trouble understanding. "What is this? Why am I using this?? WHAT DOES THIS MEAN!?!" Yeah my textbook's not very good, and the teacher didn't really go over it well. Seriously though, you're a life saver.
3rd year math major here just love you to death patrick...... been using your videos since i was a freshman and never dissapointed in your variety of subjects or skill in teaching.
From the four Newton's Method videos I just watched yours is the best by far. The visualization at the beginning was very helpful. Your video even beat The Organic Chemistry Teacher's video!
@patrickJMT We weren't allowed to use calculators, but it turns out we weren't tested on Newton's method anyway! I can't thank you enough for all your help with these tutorial videos. My math professor is absolutely horrid, and after watching these videos for the past 8 hours or so(I just got back from my exam 20 min ago after pulling an all nighter), I feel like I aced my exam. Thanks again!!
A BIG thank you from 2020! You explained Newton's method clearly and concisely, despite English not being my first language! Hope I do well on my midterm tomorrow!
Hey, Patrick, thanks for this. I am teaching Calc for the first time this year, and had forgotten how this works. Now I feel like I can explain in great detail.
I don't know what it is but UA-cam videos are almost always more helpful thank class. I appreciate you taking out your time to make this video! THANK YOU
Thanks Patrick. Really love watching your videos, they are a great supplement to my math teacher when I am at home doing my homework! I try to make your sure I give you a thumbs up every time I watch your videos.
Very very useful, better than my maths teacher really. You really know what you're saying and how to bring it across and it's simple in just under 10 minutes. Brilliant. Though we use excel to help us with it, but still this makes me understand it more rather than being alienated by TECHNOLOGY!! Cheers!!
As soon as I opened this chapter, I was so confused. But after watching your video, I understood a lot about Newton's Method. Thank you very much for the video.
Wow the introductory explanation of the purpose of newton's method was excellent. I could not visualize what the point of it was. I know it's aim is to find the root but the depiction of how it does just that made it make sense. Thank you.
the point is: what if you have a more complicated function that you can not just solve for 'x' - what do you do then?! use newtons method! i kept my function simple to: 1) illustrate the process 2) keep things simple so that i can keep the video around 10 minutes!
You could also put in your initial x value then hit STO>X. So the initial value was 3, you hit 3 STO> X then u type the function in your calculator x - (x^7-1000)/(7x^6) then at the end of that function you do STO>X, so what will be in your calculator will be x- (x^7-1000)/(7x^6)STO>X. Every time you hit the = it will take that value and make it X. Just keep hitting = until your answer is within the error limit given.
I agree with the person who said you're better than a textbook. My own textbook was over $100 as well and confuses me to no end. Thank you for these videos.
My Calc teacher is actually really good, but I'm only a sophomore in high school. I took two grades of math in the summers. So sometimes it's harder for me to grasp the concepts in AP Calc. Your videos do a really great job of reinforcing the concepts that I've learned in class. :)
i have gone through SO MANY of your videos and "liked" just about every one. haha now all my suggestion videos for my youtube account are math tutorials
Excellent video Patrick! Your video is a light unto this world, filled with the darkness caused by bad maths teachers. The geometrical insight which you give, beautifully explains the logic behind Newton's method. Of all subjects, Mathematics is populated by the worst teachers (mainly because they themselves learnt by rote). Your video is a very refreshing exception to this sad reality.
What about: 1. Version for systems of nonlinear equations 2. Picking good initial guess 3. Cases when Newton's method does not converge 4. Possible modifications to guarantee convergence
Honestly math is one of those things you have to keep on doing till you can do it with your eyes closed. Just keep on grinding and practicing then you'll do well :)
its just what it simplifies too. Try deriving it. if y=mx + b then f(x1)+f '(x1)(x1) + b. Therefore b = f(x1)-f '(x1(x1). to find the x interceot set y equal to zero you have m which is f '(x1) and b, solve for x2 :)
@fungsit In the simple case of this example an explicit solution for x when f(x) = 0 is easy, x = 1000^1/7. However, in practise you would never use this method for this type of problem. Other problems where an explicit solution is not available or where it is too computationally intensive to calculate, e.g. a large dimensional vector space problem, it is very useful. We can use Newton's method to give us a 'good' estimate of the solution in just a small number of iterations.
Thank you so much! But still can't understand what Newton's Method is good for if you can equal f(x) to zero and find the intersect x Any explanation, please?
Wow... it seems so much simpler here! Thanks so much for explaining!! But is it possible to do this without a calculator? Because my teacher's always telling us about not using calculators for problems... if we are tested on it it will have to be with calculators right??
Thanks for this video, I have found that with my calc, I work out x1. And then I replace all the xn with "ANS" and then after that I just keep pressing "=" and it spits out all the answers. Brilliant Video, Writing a test tomorrow! This will save me!
I've an exam of this subject next week and can I ask how do you knew to put x=3 in the first place to begin with. Everything else is made really simple and got hang of it.
For the function in the video, setting f(x) = 0 might be easier (although unlikely, especially doing it with a simple calculator and pen and paper, it's not easy to find the roots of that function); but if you're dealing with more complex functions you might run into some problems just setting f(x) =0... there's a reason this method exists, even though it may be obsolete in certain ways.
You should look at the function and workout a general idea where the two roots should (The easiest way to do this is to look at the graph). Then use Newton's Method twice, once with an original x value close to one 0, and another with an original x value close to the other.
+Fatima Torres Not necessarily. You want to try to pick a number relatively close because newtons method may not work for example here if you picked -3 or something way off, because the slope would be almost vertical or completely vertical and thus you would not get anywhere
Gotta love when youtube videos explain calc better than your college professor.
this is numerical analyze it's not calculus
Ye. Mine sounds like he gargles marbles. Also types on the computer one finger at a time. I often wonder how long it takes him to code...
Ya gotta love not having a calc professor... youtube becomes your only teacher... SOO effective
*chuckle* I'm only in 5th grade :) I don't get what's so difficult about this. Am I smart or are you dumb? It's simple.
Adam Shafer. Lol, you’re not smart. I’m done with math and I finished it in 6th grade. I’m current teaching my 5th grade brother. Anyone any age can finish calculus by simply indulging yourself in the mindset of perceiving ideas as easy. That’s how I finished multi variable in a month. Lol, multiple integrals and partial derivatives were just tiny pieces of CAKE!!! I also finished AP physics and AP chemistry and I’m looking forward to finishing more AP classes. I don’t know if it’s just my own idiosyncratic way of learning though, my siblings just don’t seem to understand my way of learning and memorizing. Anyways, you were just talking to an IMO (International Mathematics Olympiad) participant and a 3X Mathcounts finalist who finished all of calculus within months so...BYE. By the way, I’m not flexing.
I'm the kind of guy who relies heavily on step by step examples and equations while doing my work. The video was really helpful, I hope you make many more like this. Thanks a lot!
you save engineering students lol. I have time to hit the gym and pursue my passion for bodybuilding because I can watch your videos instead of reading through the textbook for hours lol. Gotta love UA-cam. Obviously youtube cant always grasp the level of difficulty of practice problems they give you engineering cause they make it alot harder, its still extremely helpful to understand the concept as quickly as possible instead of using a textbook lmaoo, then from there you can just practice harder problems of the same concept.
Throwback to the days when there was a time limit to these videos
Speaking of limits . . .
haha :D
Great explanation! You made me understand in 7:30 minutes what my teacher couldn't in 2 classes 1:40 hours each!
Thanks a lot!
Some night-before Calculus final cramming :)
James Cook lol I'm in this exact same position. Luckily for me, only this and parametric curves to go! yay
me too XD
Some -night- class-before Calculus final cramming :)
It's cool guys I aced it.
Same
glad you like it! i just added this one yesterdaY!
THANK YOU
"This is not the end of the world"
Wise words.
Oh thank god.
I've been studying for my calculus final (which is tomorrow) and Newton's Method is the only thing I've been having trouble understanding.
"What is this? Why am I using this?? WHAT DOES THIS MEAN!?!"
Yeah my textbook's not very good, and the teacher didn't really go over it well. Seriously though, you're a life saver.
god i wish newtons method is my only trouble...
What you upto now, 6 years later?
3rd year math major here just love you to death patrick...... been using your videos since i was a freshman and never dissapointed in your variety of subjects or skill in teaching.
Great job, my professor forgot to go over this for an exam i have tomorrow. You just saved me :D
You are amazing at explaining maths in a pedagogical way! Thank you so much for your work! The textbook that I use explained this disastrously!
Thank you! Both the Calculus textbook and my math teacher failed to explain this so that i could understand it, and you did it in about 60 seconds!
From the four Newton's Method videos I just watched yours is the best by far. The visualization at the beginning was very helpful. Your video even beat The Organic Chemistry Teacher's video!
1 minute in and I already got the concept faster than what took my prof an hour to explain
same!!!
@patrickJMT We weren't allowed to use calculators, but it turns out we weren't tested on Newton's method anyway! I can't thank you enough for all your help with these tutorial videos. My math professor is absolutely horrid, and after watching these videos for the past 8 hours or so(I just got back from my exam 20 min ago after pulling an all nighter), I feel like I aced my exam. Thanks again!!
how does your calculator find it?
A BIG thank you from 2020! You explained Newton's method clearly and concisely, despite English not being my first language! Hope I do well on my midterm tomorrow!
Thank you for all of your videos, they’ve really made a huge difference in my life by allowing me to peruse mechanical engineering.
You are literally the savior of all calc students.
You are a real lifesaver for people with professors that can't teach
Patrick, you are the reason I am passing Calc right now. You are a life saver.
Hey, Patrick, thanks for this. I am teaching Calc for the first time this year, and had forgotten how this works. Now I feel like I can explain in great detail.
happy i could help :) good luck with the teaching!
Had to quickly remember Numerical Analysis material despite being out of practice for almost 5 years. Very clear explanations and examples! God bless!
glad it helped :)
I don't know what it is but UA-cam videos are almost always more helpful thank class. I appreciate you taking out your time to make this video! THANK YOU
Thanks Patrick. Really love watching your videos, they are a great supplement to my math teacher when I am at home doing my homework! I try to make your sure I give you a thumbs up every time I watch your videos.
@TheNumber2Pencil546 thanks for liking them!
Bro you have saved my life
My calculus mid-year is in 4 days and this along with a couple other of ur vids hav gotten me a lot more confident
Cheers
Very very useful, better than my maths teacher really. You really know what you're saying and how to bring it across and it's simple in just under 10 minutes. Brilliant.
Though we use excel to help us with it, but still this makes me understand it more rather than being alienated by TECHNOLOGY!! Cheers!!
As soon as I opened this chapter, I was so confused. But after watching your video, I understood a lot about Newton's Method. Thank you very much for the video.
I mean it when i say I love you. You're a lifesaver and your teaching is the best.
I had no idea what was going on when this was discussed in class but after the first 90 seconds I think I really get it now. Thanks!
@Hackiesacker007 ha, good luck on the exam! : )
and yes, i think to actually do the computations, a calculator would be very handy.
Job well done man, i just understood something ive been trying to read the whole day in just 7:29 minutes, Thanks again man..................
well, just start by finding equations of tangent lines, and solve for the x-intercept of those lines; you will get the formula!
Wow the introductory explanation of the purpose of newton's method was excellent. I could not visualize what the point of it was. I know it's aim is to find the root but the depiction of how it does just that made it make sense. Thank you.
I have yet to find a kind of calc/engineering problem you have not yet done. Your are awesome!
the point is: what if you have a more complicated function that you can not just solve for 'x' - what do you do then?! use newtons method! i kept my function simple to:
1) illustrate the process
2) keep things simple so that i can keep the video around 10 minutes!
You could also put in your initial x value then hit STO>X. So the initial value was 3, you hit 3 STO> X then u type the function in your calculator x - (x^7-1000)/(7x^6) then at the end of that function you do STO>X, so what will be in your calculator will be x- (x^7-1000)/(7x^6)STO>X. Every time you hit the = it will take that value and make it X. Just keep hitting = until your answer is within the error limit given.
finding roots / solutions to equations is hugely important in math.
I agree with the person who said you're better than a textbook. My own textbook was over $100 as well and confuses me to no end. Thank you for these videos.
I swear to god that you've taught me more than my own proffessors. Thank you so much for being my teacher essentially! Haha
awesome, glad i could help you out a bit :)
My Calc teacher is actually really good, but I'm only a sophomore in high school. I took two grades of math in the summers. So sometimes it's harder for me to grasp the concepts in AP Calc. Your videos do a really great job of reinforcing the concepts that I've learned in class. :)
Every new concept I learn in calculus blows my mind thinking about how mathematicians created it.
thank you still the same stuff being teached in 2023
Solid video man, wish me luck on my exam tomorrow!
i have gone through SO MANY of your videos and "liked" just about every one. haha now all my suggestion videos for my youtube account are math tutorials
Thanks a lot for this video and others! I watched them all and they were a great study aid for my calculus exam earlier today!
You're the best teacher in the world ... Srsly
Nice, practical and clear teaching.
That is just amazing.. Brilliant explanation, awesome illustration and a very neat handwriting :)
Excellent video Patrick! Your video is a light unto this world, filled with the darkness caused by bad maths teachers. The geometrical insight which you give, beautifully explains the logic behind Newton's method. Of all subjects, Mathematics is populated by the worst teachers (mainly because they themselves learnt by rote). Your video is a very refreshing exception to this sad reality.
actually so much easier to understand than my 2 hr lecture
thank you so much man! i have a calc exam tomorrow and you saved me! :D
does it really matter what value you choose as your guess? will it make the process longer?
I LOVE YOU PATRICK!!!!!!!YOU SAVED ME 3 hours of insanity lol.
What about:
1. Version for systems of nonlinear equations
2. Picking good initial guess
3. Cases when Newton's method does not converge
4. Possible modifications to guarantee convergence
Thank you so much this helped me a ton. Math is not my thing but it has to be now that I'm an ChemE major fml haha
Honestly math is one of those things you have to keep on doing till you can do it with your eyes closed. Just keep on grinding and practicing then you'll do well :)
@hellosoul22 degree two polynomial - use the discriminant
its just what it simplifies too. Try deriving it. if y=mx + b then f(x1)+f '(x1)(x1) + b. Therefore b = f(x1)-f '(x1(x1). to find the x interceot set y equal to zero you have m which is f '(x1) and b, solve for x2 :)
If it weren't for your UA-cam tutorials and Wolfram Alpha, I'd have failed college calc without doubt. Thanks man.
for the first example, where did you get the 3 for the first x? thank you for the answer :)
no problem
@fungsit In the simple case of this example an explicit solution for x when f(x) = 0 is easy, x = 1000^1/7. However, in practise you would never use this method for this type of problem. Other problems where an explicit solution is not available or where it is too computationally intensive to calculate, e.g. a large dimensional vector space problem, it is very useful. We can use Newton's method to give us a 'good' estimate of the solution in just a small number of iterations.
Thank you so much!
But still can't understand what Newton's Method is good for if you can equal f(x) to zero and find the intersect x
Any explanation, please?
Wow... it seems so much simpler here! Thanks so much for explaining!!
But is it possible to do this without a calculator? Because my teacher's always telling us about not using calculators for problems... if we are tested on it it will have to be with calculators right??
Way easier to understand now! Thanks!
do you also have tutorials for fixed-point iteration method?
Can we use 1 for n or do we have to use 3? How do you approximate the number?
Thanks for this video, I have found that with my calc, I work out x1. And then I replace all the xn with "ANS" and then after that I just keep pressing "=" and it spits out all the answers. Brilliant Video, Writing a test tomorrow! This will save me!
much better than my analytical techniques lecturer!
Thank you you are like my 2nd calculus tutor, my calculus teacher does not teach well
thanks dude.. helps me a lot in my final exam..
of course... but can not one do just about all of math now with a calculator?
Great video - much easier to understand than my lecture notes! Thanks so much!
"Did you Know?: This method is actually named after 'Fig Newtons' cause it is so sweet!
Take that Sir Isaac!"
is the point where it intersects the x value where when u cslculate it it gives the same result as before??
Thanks for these videos!! Helps so much!
thanks!
I've an exam of this subject next week and can I ask how do you knew to put x=3 in the first place to begin with. Everything else is made really simple and got hang of it.
Edit: So 3 gives positive solution but how do you find that out? You just try several numbers and test how they act?
You pick a starting value that you think is near the root. It's an approximation/guess.
rawritshien Thanks!
it is an initial guess he put 3 because 3 is close to the root.
Hypixel King Thanks!
how do you know the root must be between 2 and 3 at the first time? I dun really know which no i should pick for x1?
good luck!
For the function in the video, setting f(x) = 0 might be easier (although unlikely, especially doing it with a simple calculator and pen and paper, it's not easy to find the roots of that function); but if you're dealing with more complex functions you might run into some problems just setting f(x) =0... there's a reason this method exists, even though it may be obsolete in certain ways.
OMG thank you! The first min was already enough ^^
Same here! I was reading the the book for like 15 mins, couldn't understand what the hell it said there. His video did help!!
Can you please make a video for newton's laws of cooling?
hey mr patrickJMT! is this the same as fixed point iteration?
wow that was a lot easier than i thought it would be. Thanks man!
Can you use this to find y intercepts or to find any other intercepts at x = n or y = n?
You are a math god and I owe you my sanity
You should look at the function and workout a general idea where the two roots should (The easiest way to do this is to look at the graph). Then use Newton's Method twice, once with an original x value close to one 0, and another with an original x value close to the other.
Would you have gotten the same answer if you plugged in 2 instead of 3?
Hi i was wondering how can u find two positive roots using this method? I have an exercise to do which requires that
also referred to as newton-raphson method ?
YES (answering so future viewers can know).
thanks man. I hope a lot of good things hapen to you
FINALLY I GET THIS. THANK YOU. probably still going to fail tomorrow, but at least i know something
Great video. Simple to understand.
Please could you make more linear videos: orthogonolisation, Cauchy-Schwarz, Gram-Schmidt, eigenvectors etc. thanks
Can I plug in any number that is greater than or less than the x intercepts into the equation?
+Fatima Torres Not necessarily. You want to try to pick a number relatively close because newtons method may not work for example here if you picked -3 or something way off, because the slope would be almost vertical or completely vertical and thus you would not get anywhere
So newtons method is a repitition of linear approximation?