i AM the organization : ) just math tutoring , patrickjmt, president CEO yes, i have spent hundreds and hundreds of hours making these videos; when people make a donation, it goes straight to me. i take it as a huge compliment, as in this day and age, who actually pays when u can just get it for free?! : )
My final is tomorrow, and I have done nothing but study your videos, my friend. You have helped me to not only pass this course, but to truly understand the material. Thanks for a great year in calculus, Patrick.
@1337Bigman no, if you use a different number, you will get a different approximation cause you will get a different tangent line to use as an approximation
hey patrickJMT, you're a lifesaver. It's 2:20 in the morning and I was studying for a test and I had no idea how to work it. Then, I watched this video and now it makes worlds of sense! Again, THANKS!
this is also why my videos are now appearing in HD - youtube started allowing this so i took the donations that i had to get a better camera! so partly, it just goes back to the viewers anyways!
Your videos are really great! I watched many videos during my calc. class and right now to review for our final. Thank's for making these great lessons. :) Also ..... I just realized you are left handed after watching so many videos, and I watched about 10 already, lol
Thank you so much! My teacher said we are not really having a lesson on this section in class tomorrow but rather working through it on our own, so thanks for being the substitute lesson!
agh, thanks so much// Everyone was so tired in math yesterday and we have a quiz tomorrow and I had no idea what she was going on about anymore, so thank you
In Canada, Maths isn't taught with application early on, so later uses when it is applied like in Algebra (word problems), people despise it. Once you get into a physics class you apply this. Not to mention if you're a business major this is used in business calculus. In Germany, most Maths are applied or related to a real world example, as if you don't pass early on your off to a trade school. No point in teaching someone something they don't want to learn.
I would've mentioned that were using the "point of the number that's hard to evaluate" on the tangent line of the graph at the "point that's easy to evaluate" and shown what dy is graphically
my exam is tomorrow, so hopefully you'll see this. at the beginning, you gave us the equation to find dy. at the end, you added dy to the original y value, which was 2. so, to get the true change in value, is the equation dy+f(x) ???
I got confused when you were calculating dy (16^(3/4)). Could you explain why it is legit to cube the fourth root of 16? I have never seen that done before. I have been doing that on my homework problems but have no idea why it is a legal algebraic step. Would appreciate reply!
this is simply one side of them. they are essential to the concept of an integral, as well as providing some intuitiveness to other calculus concepts (i.e. dy/dx).
So this is pretty much a fancier way of doing linear approximation? There's no difference in the final approximations when comparing it to the value of L(x) when x = 18.
so what exactly is the point of differentials and linear approx? they only give approximations of numbers we can put into a calc. do differentials have some other use?
Well way back when calculators weren't really beneficial, if you think of all these theorems we cover in calculus (1-3) [im in calc 3] majority if not all were developed by hand and build off of each other. approximations by differentials were and still are acceptable values because of their range to the actual answer...the arithmetic is also a lot cleaner if you work with complicated functions. Also reassuring that the correct answer should be around that value if executed correctly. The hardest part about Calc is not the Calc part...its algebra, and learning all these theorems are ways to show that you are capable of solving problems by applying what you know. It makes you that more capable of landing a job bc you now have the power to estimate the value. If we cant do math without a calculator how do we expect to be better than the generations before that didn't have them xD
liverpooler1997 lol nicely said.. Well America is in a huge need of stem researches. And America isn't the only country with freedom xD we just think so highly of ourselves when in reality were probably only proud of our money. Anyways another huge debate topic xD lol. Keep going mate math is awesome
That is what college is for. If you (anyone in general) are taking a calculus class, and you don't plan on a math major, you are doing something wrong. If you're college requires it, then they are probably trying to make sure you are competent enough for them. What most people would consider "real world math" is highschool math.
so if u differentiate the f(x) function, you would get dy/dx= 1/4x^-3/4. you can rewrite it by moving the dx to the right, so it is dy=1/4x^-3/4 times dx
i have a crush on patricJMT, too bad he is married! thanks for all the help.i get A's on my calculus exams thanks to you.&that's saying something because our professor gives us problems that make other professors cringe.closed book exams with no note card or cheat sheets.for our last exam, we had to memorize all the the derivatives to the trigonometric functions along with their inverse counterparts.next i have to memorize all the hyperbolic functions and their derivatives! thanks again Patric!
+Killer97 Although that will suffice for most of the beginner calculus course, please note that dy/dx is not a fraction. You cannot multiply both sides by dx but it works in this case
Sure- delta x (delta is the triangle) is "the change in x", or "the change between the old x and the new x", if that makes any sense. dx is simply an approximation of delta x- you know how we say 1.99999 is the same thing as 2? This is the same thing.
Wait so what is the point of this if you end up getting 33/16? You still don't know what the decimal value it is haha and I thought that was the whole point of differentials?
i AM the organization : )
just math tutoring , patrickjmt, president CEO
yes, i have spent hundreds and hundreds of hours making these videos; when people make a donation, it goes straight to me. i take it as a huge compliment, as in this day and age, who actually pays when u can just get it for free?! : )
My final is tomorrow, and I have done nothing but study your videos, my friend. You have helped me to not only pass this course, but to truly understand the material. Thanks for a great year in calculus, Patrick.
@1337Bigman no, if you use a different number, you will get a different approximation cause you will get a different tangent line to use as an approximation
hey patrickJMT, you're a lifesaver. It's 2:20 in the morning and I was studying for a test and I had no idea how to work it. Then, I watched this video and now it makes worlds of sense! Again, THANKS!
My final is in 5 hours and you my friend have saved my life once again on another test. Bless your soul!
I unfortunately slept through the calculus lecture when my class learned this information. This video saved me! Thanks!
(32/16) + (1/16) in the last step brotha :)
I tried to understand this from a MIT professor, But you did a hell of better job !
the nueral net video?
Your the best teacher in the world; special thanks from Portugal.
this is also why my videos are now appearing in HD - youtube started allowing this so i took the donations that i had to get a better camera! so partly, it just goes back to the viewers anyways!
Your videos are really great! I watched many videos during my calc. class and right now to review for our final. Thank's for making these great lessons. :)
Also ..... I just realized you are left handed after watching so many videos, and I watched about 10 already, lol
Patrick you are a very talented math professor, I feel fortunate to be able to watch your videos. Thank you.
Thank you so much! My teacher said we are not really having a lesson on this section in class tomorrow but rather working through it on our own, so thanks for being the substitute lesson!
thankss patrick you've helped me through most of calc 2 and 3. you're superman in the math world
i would love to see more linear approximation examples!
@gengen23100 yes, that is the general idea
To get from x=16 to 18 we had to add 2. Therefore, dx=+2.
thank you veyr much I was sick and missed a lot of differentials but now I think i understand
this guy never fails me
FINALLY!!! Someone who can actually explain this ****
THANK YOU!!
Thanks for saving me the headache right now. Much love man!
agh, thanks so much// Everyone was so tired in math yesterday and we have a quiz tomorrow and I had no idea what she was going on about anymore, so thank you
@CollegeboundGaming i think that is a perfect way to use these, glad it is helping a bit :)
Every time you make a mistake and cover it with annotations, an angel gets its wings.
In Canada,
Maths isn't taught with application early on, so later uses when it is applied like in Algebra (word problems), people despise it. Once you get into a physics class you apply this. Not to mention if you're a business major this is used in business calculus.
In Germany, most Maths are applied or related to a real world example, as if you don't pass early on your off to a trade school.
No point in teaching someone something they don't want to learn.
I would've mentioned that were using the "point of the number that's hard to evaluate" on the tangent line of the graph at the "point that's easy to evaluate" and shown what dy is graphically
I want to know have you made a video on the tangent and velocity. I know you did one on tangent but what about for finding the a(t), v(t), and s(t).
Had to watch the video twice, but I get it now. Pretty neat!
youre easier to understand than my professor. thank you!
Five years dude!
i did.
you got an unusually fast turn around : )
my exam is tomorrow, so hopefully you'll see this.
at the beginning, you gave us the equation to find dy. at the end, you added dy to the original y value, which was 2.
so, to get the true change in value, is the equation dy+f(x) ???
very very clear!!!!! Patrick you're DAREALMVP!!!!!
Great video! I am crystal clear on this topic now.
awesome, I didn't know you could do that with differentials..
oh and by the way, at 6:35 when you're simplifying 2 + 1/16, you write 2 as 32/2. :P
thank you so much i was having trouble finding an approximation until i found ur solution
I got confused when you were calculating dy (16^(3/4)). Could you explain why it is legit to cube the fourth root of 16? I have never seen that done before. I have been doing that on my homework problems but have no idea why it is a legal algebraic step. Would appreciate reply!
Why you haven't take change in x value approaches to zero for corresponding change in y values. Plz reply
idk if u noticed but u put 32/2 at the end when its 32/16... because you need common denominators to add the fractions.
correct
So differentials are essentially used to approximate the answers to problems we are typically unable to solve? Or is this just one side of them?
this is simply one side of them. they are essential to the concept of an integral, as well as providing some intuitiveness to other calculus concepts (i.e. dy/dx).
Thanks Patrick!!! You are awesome!!! keep up the good work!!
@TheNumber2Pencil546 that's what she said (about you)
woot! great video =D! thats all I needed for my test
So this is pretty much a fancier way of doing linear approximation? There's no difference in the final approximations when comparing it to the value of L(x) when x = 18.
It's a way that's easier for more complicated functions.
thank u man this helps a lot!!!
if you are only given an equation and are told to find the differential... how do you do that?
so what exactly is the point of differentials and linear approx? they only give approximations of numbers we can put into a calc. do differentials have some other use?
Well way back when calculators weren't really beneficial, if you think of all these theorems we cover in calculus (1-3) [im in calc 3] majority if not all were developed by hand and build off of each other. approximations by differentials were and still are acceptable values because of their range to the actual answer...the arithmetic is also a lot cleaner if you work with complicated functions. Also reassuring that the correct answer should be around that value if executed correctly. The hardest part about Calc is not the Calc part...its algebra, and learning all these theorems are ways to show that you are capable of solving problems by applying what you know. It makes you that more capable of landing a job bc you now have the power to estimate the value. If we cant do math without a calculator how do we expect to be better than the generations before that didn't have them xD
Blitzkrieg NvME this is america, we dont need math,,, we need freedom. jk, yeah i guess youre right. im in calc 1, but im a high schooler.
liverpooler1997 lol nicely said.. Well America is in a huge need of stem researches. And America isn't the only country with freedom xD we just think so highly of ourselves when in reality were probably only proud of our money. Anyways another huge debate topic xD lol. Keep going mate math is awesome
That is what college is for. If you (anyone in general) are taking a calculus class, and you don't plan on a math major, you are doing something wrong. If you're college requires it, then they are probably trying to make sure you are competent enough for them. What most people would consider "real world math" is highschool math.
Thanks, Patrick!
i WATCHED the video once.. got it... next one!! So either I;m a genius or you're that good.
why is the change in x positive and not negative? do you think you can briefly explain to me the reason for this.
it is positive because x is increasing. from 16 to 18. if it is decreasing then it is negative
So essentially , dy = f ' (x) dx ?
That is it?
duh, thanks, i tried to add fix it : )
see you have a wedding band. damn. not like we would've ever met anyway... and i'm probably too young for. sorry we couldn't work out, patrick.
Why do you multiply 1/4x^-3/4 to dx? Where'd that come from?
so if u differentiate the f(x) function, you would get dy/dx= 1/4x^-3/4. you can rewrite it by moving the dx to the right, so it is dy=1/4x^-3/4 times dx
Thats the derivative of x^1/4
(Using chain rule)
thanks guys!
If dx is the approximate change of x why do you say it equals 2 when 2 is the actual change of x??
i have a crush on patricJMT, too bad he is married! thanks for all the help.i get A's on my calculus exams thanks to you.&that's saying something because our professor gives us problems that make other professors cringe.closed book exams with no note card or cheat sheets.for our last exam, we had to memorize all the the derivatives to the trigonometric functions along with their inverse counterparts.next i have to memorize all the hyperbolic functions and their derivatives! thanks again Patric!
Im doing practice problems off kuta software and one problem says y = x^3 -2 and apparently the answer is ∆y = −3x^2(∆x) − 3x(∆x)^2 − (∆x)^3. Why?
thanks Patrick.
Where did the equation from dy come from?
+erccool f'(x) = dy/dx therefore by using algebraic rules dy = f'(x) * dx
you are just multiplying both sides of the equation by dx
+Killer97 Although that will suffice for most of the beginner calculus course, please note that dy/dx is not a fraction. You cannot multiply both sides by dx but it works in this case
it is ok. it seems that scientists have found a way to clone it, as i see lots of them at the store for sale
Thanks! Good job
how did you get the 32/16? help!! i have an exam next week
2 = 32 / 16
i salute u n ur videos
thanks alot
How come dx=2?
Can I think it as delta x ? Is that what it meant?
Sure- delta x (delta is the triangle) is "the change in x", or "the change between the old x and the new x", if that makes any sense. dx is simply an approximation of delta x- you know how we say 1.99999 is the same thing as 2? This is the same thing.
Thank you! : D
You are the best!
Last step you wrote 32/2 but of course you meant 32//16 , because the total eas 33/16
Thank you, I'm now ready for my test in 5 hours :\
so "dx" is the change of your actual number and the number you picked. :D
Shouldnt it be 257/16 and not 33/16?
Actually nevermind it should be 2 + (1/16) which is (32/16) + (1/16) = 33/16
@patrickJMT you mean the 4th root of 16
thanks again!!!
@gengen23100 just use the taylor serie.
@DanIsSoKrispy cause i know the square root of 16
thank you sir
THANK YOU!!!
dy=f''(x)*dx
That's what he was saying at the beginning.
@joshuayyc
PatrickJMT always on point.
you just saved my life! lol
Sorry to hear about your pen dying.
newton's method of linearization...
euler's method is diferent.
how did he manage to know that x=18 in the first point?
math makes me go limp
Good stuff! sub'd
Tysmmmm my lorddd
wow ur so smart! thanks
thanx
does anyone know what patrickjmt looks like? hahahahhahahahahah
dude if you are still alive, wouldnt it be negative two? because you went from 18 to 16
Wait so what is the point of this if you end up getting 33/16? You still don't know what the decimal value it is haha and I thought that was the whole point of differentials?
@patrickJMT lol
@patrickJMT haha touche