Using Differentials

[SecondVelocity]

Thanks! My AP Calculus AB/BC Exam is tomorrow (the teacher made) and this really helped!

[Floydfan101]

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) ???

[tastynuggets21]

thank you based patrick

[hadoolket]

i'm too lazy to check if anyone else mentioned it, but it looks like you made a small error as putting 2 = 32/2 instead of 32/16, even though you did the calculation correctly otherwise

[lucuador1992]

you are really helping me out! I have a midterm in 5 hours and i lost all hope because my professor decided to teach us 3 new topics in one day so he can put it on the midterm. 3 topics in 1 hour + my professor's THICK accent = no hope whatsoever -.-

[girlletyourhairdown]

My goodness! Thank you so much, my math teacher never explains anything and you are seriously a life saver!!

[TheNumber2Pencil546]

math makes me go limp

[patrickJMT]

@TheNumber2Pencil546 that's what she said (about you)

[TheNumber2Pencil546]

@patrickJMT haha touche

[1337Bigman]

@patrickJMT So, for the sake of argument, could you have chosen a different number for x, something besides 16, and still get (33/16)?

[patrickJMT]

@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

[DanIsSoKrispy]

@patrickJMT So then why did you use 16?

[patrickJMT]

@DanIsSoKrispy cause i know the square root of 16

[joshuayyc]

@patrickJMT you mean the 4th root of 16

[yucky1336]

thankss patrick you've helped me through most of calc 2 and 3.  you're superman in the math world

[z0j3]

I wish i can disklike the one who disliked the video

[shelteringshade]

this definitely helps me out with thermodynamics!

[mrjost55]

Thank you, I'm now ready for my test in 5 hours :\

[swatregret]

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.

[demonangels67]

@patrickJMT My messiah in math,

Im gonna fail in math but I glad I found this so next time I'll take that course I'll own >:D hahahaha

[3darien]

Patrick you are a very talented math professor, I feel fortunate to be able to watch your videos. Thank you.

[xTheLeaderx]

THANK YOU!!!

[renzokukenleonhart]

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).

[pimpmymail]

ull help me pass my uni. exam today lol :D Im graduating of the youtube university it seems, thanks to u all :D

[gengen23100]

I have a question

whenever you have (8.2)^1/2 to approximate, do u always have to pick the closest number that you know the square root of? for example, I know that the closest value that I know the square root of is 9 but what if it initially i didn't do it that way and I did the problem using the square root of 4. my point is when I approximated 8.2 & used the square root of 2, I got the wrong answer & when I used the square root of 9 i got the right answer. is it always the closest you pick?

[patrickJMT]

@gengen23100 yes, that is the general idea

[gengen23100]

@patrickJMT awesome. thanks a million! :))))

[gengen23100]

@patrickJMT awesomee. thanks a million!! :))

[gengen23100]

@patrickJMT awesome. thanks a million! :)

[BeenuZz]

@gengen23100 just use the taylor serie.

[gengen23100]

the fact that we are not allowed to use calculators (im in Calc I) during exams but since now i that you've taught me how do it this way, I won't have to not answer the questions about approximations. THANK YOU ONCE AGAIN!!!!!! :) YOU"RE THE MANNN!!

[gengen23100]

Thank you so much. This video really helped big time. My professor very much enjoyed to complicated things like this, thats why half of the class is failing. Thanks to you I won't be one of them. THANK YOU THANK YOU AGAIN! I cannot thank you enough! God bless you! :)

[sugrwatrpurplee]

youre putting me through college as much as my parents are. greatly appreciate it.

[akorabful]

my condolences for your pen :'(

[akorabful]

<3 u

[ScotleCyphez]

i don't know why but for some reason these are fun to do O.o

[stagpeacebringer]

Cool video, it is nice to see stuff like this on youtube.

[Oblisk47]

So essentially , dy = f ' (x) dx ?

That is it?

[eversmann85]

Do you have anymore examples on differentials?

[warlocks4life]

Thanks a lot man. This is the exact problem I had on my homework, verbatim!!

[YourAccountNameHere]

thank you, sir.

[starwarsfreakdood]

You should teach this to all the Calc teachers in Amercia because they need help major help teaching this!! :)

[cantabriver]

Thanks alot

[Hotdogbunker]

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!

[TiduStrife007]

correction: in the last part (right before calculating 2+dy), 2= 32/16; not 32/2.

the answer you arrive at is clearly correct, but i just wanted to point out that small error there cause it might confuse people.

[MrJacobrodgers]

Wonderful. Well done, my fog of confusion is starting to clear.

[KiddyBrucie15]

Could you post more videos of linear approximation? I never understood it that well when our teacher went over it and when others explained it they just made it more confusing.

[trunker420]

i would love to see more linear approximation examples!

[trunker420]

thanks again!!!

[equihua]

woot! great video =D! thats all I needed for my test

[Syruscleat]

Sorry to hear about your pen dying.

[patrickJMT]

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

[elight07]

@patrickJMT lol

[Physicsandmaths]

Had to watch the video twice, but I get it now. Pretty neat!

[chandralekha16]

i think this is also called the Euler's Method (which i knw is a part of the AP CALC BC syllabus)

well... at least it seems somewhat like it!

[xelink]

newton's method of linearization...

euler's method is diferent.

[stmc247]

i still prefer my calculator. LOL. but still i never knew we can use differenciation to approximate a value. thanks!!

[yoyaya007]

thank u man this helps a lot!!!

[eedahl]

Nice! I didn't know one could do that. I like how differentials lets you reason algebraically, pretty intuitively. You mentioned "change in x" for the triangle delta. I figured you might find something I just read somewhat interesting. In a physics book the author pointed out that "change in x" should be read as "increase in x", so as not to confuse it with just any change when that makes sense. Then you have a very useful concept of increase, and negative increase without being ambiguous.cheers

[cosmicism]

i freaking love you

[mactechnodude13]

using differentials to approximate change....does that mean we can use differentials to track the change Obama has done? lol jk great video, as always :)

[cesfigas]

Your the best teacher in the world; special thanks from Portugal.

[jhonma1]

thanks Patrick.

[Nickzed]

if we donate through that JustMathTutoring website, do you see any returns from that or is it just to the organization itself? seems like it would probably take a good chunk of time for you to make these and they help a lot of people, should be a way to show appreciation to you specifically through donations or something

[patrickJMT]

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?! : )

[patrickJMT]

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!

[srslayerz]

wow ur so smart! thanks

[JustSemantics]

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

[patrickJMT]

duh, thanks, i tried to add fix it : )

[AtlantiXYL]

i got it now

[ZergFireX]

Wow... I feel like you posted this in response to the comment I left on your channel... Thank you so much, I'm sure it'll become clearer after watching the video again and doing some problems in my book. :)

[patrickJMT]

i did.

you got an unusually fast turn around : )

[ZergFireX]

That's awesome :D