I'm in calc 2 here at UMass and my professor is not the best at explaining this. But you go into detail and thought process for each step and because of this video I now understand what my professor has been trying to teach us for the past two weeks. Thank you.
@desertfox1792 Look carefully. On the right side, the 2 in the numerator cancels the 2 in the denominator. What is left is exactly equal to the left side. Hence, no error ;)
For the series, it starts at zero. So the first term would be (2x)^0 = 1. If you take the derivative of the series, wouldn't it mean the same thing as taking the derivative of the values? The derivative of 1 would be 0. Therefore n should still start at zero. Correct me if I'm wrong.
Hey Patrick, do you have a video where you find a definite integral? The only question I have is say that our limits on our integral are 0 and 0.2. After finding what the integral is, do I plug in 0.2 in for x or n? Please reply asap bc I have a test tomorrow morning. Thanks!
Seriously?!?!?! Patrick, you are the lifesaver of upper level mathematics. My book "explains" this step by step but they forgot we speak english, not some foreign out of this world language, thus the reason why I couldn't do my homework for almost a week of trying to learn this stuff. I watch this vid once%2φ
Hahaha, I thought my phone was ringing and then the akward silence when you weren't speaking made me realize it was yours. Made me feel like an idiot, lol.
@MrSoysauce2rice plug the radius of convergence that you got back into your originial power series and test for convergence or divergence using one of the tests. If its convergent, you put a bracket and if its divergent you put a " ( " . So, its a x,y point where x = -R and y = +R .
How do you know when you move the lower bound of the sum upwards or downwards? Like when you differentiate or something, you bring the lower bound n (of the sum) up one or so.
Oh my goodness! I started laughing so hard when I heard the phone start to ring and even harder when you ran to silence it. Those footsteps were priceless. By the way, did I give you that t-shirt idea or were you gonna do it anyway?
@patrickJMT I've been watching Khan Academy for the last few months. You really picked up where he left off in the Calculus series. I'm totally a Patrick JMT convert and tell everyone in my calc class about it. I really think if you were to collaborate, it would take the educational community by storm. Thank you for all you do here! I will definitely donate to the cause as soon as I'm not a terribly poor college student!
@patrickJMT You were there for us in some of our darkest and most desperate times of need. You are helping future scientists, doctors, engineers(me), and mathematicians. These are the people who are going to be forging a better path for humanity. You are helping mankind progress and the world will be better for it. Thank you Patrick.
Thanks for the video. That was pretty cool seeing how you could manipulate a function to get the power series representation. It probably does take more examples to get used to it, and I'm all for more seeing more examples.
i see what you did at 3:00, you differentiated the summation itself. what we were taught to do was, write out a few terms of the series, differentiate each, and find a pattern so you can write it in general form.
Excellent videos man! Like many others I'm stuck teaching myself because my actual professor, and I use that term loosely, is useless. Thanks to you, and others like you, I'm actually making sense of this stuff. So thanks again, and if possible I wouldn't mind seeing some more examples on this subject. Cheers!
Hey, for the second question you did; what if you got c to equal a number.. then if you subracted it from the equation you got to make it look like the original question it wouldn't be a power series anymore right? so what would you do? and btw thanks so much patrick for providing us with so much help.. it means a lot to me and everyone else.
Hi great videos, As of last week I started studying "sequences and series". Again, the branding chosen inappropriate and unnecessarily confusing , not distinguishable at all. I would leave "sequences" as it is but would refer to "series" as "add-series" or better yet "add-sequence or sum-sequence" simply because now, in the word the clue of summation already has been giving in the initial descriptive sense.
Hi thanks for the vid. A question though. Why dont you shift the index by replacing n with n-1 in integration, much like how you replace n by n+1 in differentiation?
i've been watching all of your calculus videos since my midterm, since then my grade has gone up TWO LETTER GRADES. Tomorrow morning is my calculus 2 final and if i make an A on it i make an A on the course. i dont wanna jinx myself but ive been studying like crazy with the help of your videos so i feel good. If i get an A i will donate my life savings to you and name my first child patrick. no lies.
@Jawshooah I was going to ask the same thing. I really couldn't understand how 2^n was a constant as well. But I guess since we're taking the derivative with respect to x, that would truly make 2^n a constant. Otherwise, if x was the constant, the derivative of x^n would not be nx^(n-1) but x^n*ln(x).
Wait.. So, Patrick. You're saying you started out with Pre-calc in your sophomore year, of COLLEGE?? Dude.. I've been taking calc since my sophomore year of HS and it still intimidates the hell outta me. Your videos help to clear a lot of it up though. Thanks!
@iYoungJ89 yes, i believe it was my sophomore year (actually, it may have been the summer between freshman and sophomore year). but i came to math relatively late in life i think
Thank you so much for putting up these videos, as a freshman in college in calc two with a test on Monday, I really appreciate your explanations of series. You're the best!!
You saved my life man, my parents wouldn't let me play Starcraft 2 because i couldn't do my homework on this. Thanks to you I was able to complete my homework and now I can play Starcraft. You are the best ever!
ommmmgggg wtf was that?!?!?! All that was just like.....woooaaaaahhhhhh, so crazy. I didn't understand what my professor was talking about when he did this lecture this morning. But after watching this, I actually kind of understand it now : D. I just have to watch this a couple of more times to fully understand everything. Thank you for making everything much simpler to understand!
Patrick! What can I say, man, except you rock! I am taking an online calc II course with very little contact with the instructor but need to the course to get into my grad school that starts in sept. I would, without a doubt, be miserably failing this course without all your videos. You shine light in dark places, bro. Much appreciated!
if you integrate the original f(x) then find a power series representation for the integral of f then differentiate that power series you should get the same answer?
I'm sorry but I still don't understand what happens with the plus C after you integrate..how DID you managed to get rid of it? From the video, it seemed as though you took an arbitrary value of x and solved for C at that point..sorry if this doesn't make sense..I just want to know what happened with that +C after integration and how to approach similar situations in questions
my school is absolutly not preparing me for college...especially in calc...what happens if I screw up in college bc of a lack of knowing calc before I get to college?
well, you, like many others, will have to either retake it, or taking some to prepare you for the class.
this was the same sh*t hole i was in... my school was a total joke. i skipped about 50% of my days as a high school senior but still made A's in everything.
i had to start with precal myself in college (sophomore year)...
@patrickJMT I am studying to become a math instructor. What would make calculus better in a classroom? Although I have an excellent professor, I do most of my learning on my own and with the great help of your videos.
@YBPhotoeditor06 You can always go to a junior college to do generals(it's convenient bc its cheaper) and in 3 semesters(algebra, trigonometry, calculus 1), you can be good to go in calculus 2, 3, linear algebra, ode, proofs, etc.
@YBPhotoeditor06 dont worry about it. i didnt take calc in high school, i didnt even take math my senior year. i made an A in calc1 at LSU. although i studied my ass off . it just takes a lot of work, but you can do it
@t3nd10usx Hmmm.... Notice the PLEASE at the beginning of my request. Let's define please. Please: used in making polite requests and in pleading, asking for a favour, etc. Example: "please pay attention" So, PLEASE go somewhere w/ that.
for the problem in which you differentiated 1/(1-2x), how would you find the radius of convergence of that? Is it just one? I'm doing my math homework now and I had a very similar problem however, it was telling me that the radius of convergence was not one.
Why is it that when you differentiate a series the index of summation increases by one, but when you integrate a series the index of summation does not change?
yo patrickJMT, that was indeed a gr8 help for my finals, thnx a ton man. I needed this help bcz I missed the class for this lecture and this tutorial saved my time , thnx a ton once again.
i think you did this one wrong....when you take out the (-2x)^2 you keep it as (-4x^2) but it should be (-2)^2 * x^2 giving +4x^2 so the (-1)^n shouldnt be there....correct me if im wrong...
I think it is because if you write out the series before the derivative is taken you'll see a constant at the front. when you take the derivative of a couple terms, it'll still have a constant and to you have to set the series notation for the derivative to start with a constant so that they agree...I think...you should wait for confirmation of others.
Why does my instructor make this so complicated?!? Why can't they just show me examples like this? It's not like your making this easier than it really is, because I've been doing 95% on my tests based on these videos.
Regarding changing the index, it has to do with the fact that if you differentiate a constant, it becomes 0. So the first term is gone, so you change the index to reflect that. As for the radius of convergence, all power series converge at x=c if they converge at all. Since c=0, in this case, he is using that. The important part here is simply that he needed one point to solve for C. You can use any point, I believe, and it should work. 0 is just the easiest in this case.
The most enthusiastic teacher I've ever seen. You turned off your phone, which rang during the seminar to keep it going. Even my passionate teacher doesn't do that. PATRICK JMT ROX!!!!!!!!!
Anyway, how do we show that S(1/n) (summation of 1/n as n goes from 1 to infinity) diverges extremely slowly? We can't do it using Test for Divergence.
well, you can show it diverges through an arithmetic argument; to show that it diverges 'slowly'... what does 'slowly' mean? i agree.... if you add up terms... lots and lots and lots and lots of them, you still getting a pretty small number
your video is great/ I wish you were my calc teacher!!!!!!!!!!!! you should definitely think of moving to Illinois and teach math here!!! *around 2:50 I am kind of confused too D: can anyone explain why he changes the index 0 to 1? D: *
I am a little confused... I have seen this a couple times so obviously I am missing something... you say that the derivative of 1/(1-2x)=2'/(1-2x)^2 now... wouldn't you use the quotient rule? 1'(1-2x)- haha nevermind
Your videos have helped me so much. I'm a freshman in high school and have just taken the calculus placement exam and it was easy thanks to your help! I'm still very nervous because I'm waiting for the results.
I swear math is like magic...
kenikozo 2 days ago
@kenikozo it is pretty amazing stuff. i wish i was smarter and less lazy so that i understood more of it :)
patrickJMT 4 hours ago
This video definitely helped a lot! I like how you got right to the point instead of drawing out useless information like some videos!
katherine55100 5 days ago
@katherine55100 always a fine balancing act between showing too much and showing not enough. :) i do my best!
patrickJMT 3 days ago
hopefully u can do more examples on this type of questions
heat3 3 weeks ago
Khana < rootmath < Patrick JMT
That's just how it goes...... ;)
eyekantbeme 4 weeks ago in playlist Calculus 2 PatrickJMT
this one is hard :(
RIOLITE1 2 months ago 2
I'm in calc 2 here at UMass and my professor is not the best at explaining this. But you go into detail and thought process for each step and because of this video I now understand what my professor has been trying to teach us for the past two weeks. Thank you.
AtheylStarcraft 3 months ago
wonderful. You are going to heaven my friend.
Billabong024 3 months ago
4:30 how can you randomly put x^2/2 on the right side without doing it to the left?
desertfox1792 3 months ago
@desertfox1792 Look carefully. On the right side, the 2 in the numerator cancels the 2 in the denominator. What is left is exactly equal to the left side. Hence, no error ;)
foundede 3 months ago
For the series, it starts at zero. So the first term would be (2x)^0 = 1. If you take the derivative of the series, wouldn't it mean the same thing as taking the derivative of the values? The derivative of 1 would be 0. Therefore n should still start at zero. Correct me if I'm wrong.
NomCerealNom 3 months ago
Hey Patrick, do you have a video where you find a definite integral? The only question I have is say that our limits on our integral are 0 and 0.2. After finding what the integral is, do I plug in 0.2 in for x or n? Please reply asap bc I have a test tomorrow morning. Thanks!
caligal2010 3 months ago
Seriously?!?!?! Patrick, you are the lifesaver of upper level mathematics. My book "explains" this step by step but they forgot we speak english, not some foreign out of this world language, thus the reason why I couldn't do my homework for almost a week of trying to learn this stuff. I watch this vid once%2φ
caligal2010 3 months ago
Hahaha, I thought my phone was ringing and then the akward silence when you weren't speaking made me realize it was yours. Made me feel like an idiot, lol.
caligal2010 3 months ago
Didn't make sense.. till i started solving the problem too.
Any idea how to solve for the interval of convergence ?
MrSoysauce2rice 3 months ago
@MrSoysauce2rice plug the radius of convergence that you got back into your originial power series and test for convergence or divergence using one of the tests. If its convergent, you put a bracket and if its divergent you put a " ( " . So, its a x,y point where x = -R and y = +R .
caligal2010 3 months ago
You are awesome! I was just about to give up on my homework, but I think I get it now. Thanks for putting this up!
Duhhh233 3 months ago
Thank you so much Patrick, your videos are so helpful.
adrukker 3 months ago
How do you know when you move the lower bound of the sum upwards or downwards? Like when you differentiate or something, you bring the lower bound n (of the sum) up one or so.
neogeo328 4 months ago in playlist Sequence and Series Video Tutorial
Oh my goodness! I started laughing so hard when I heard the phone start to ring and even harder when you ran to silence it. Those footsteps were priceless. By the way, did I give you that t-shirt idea or were you gonna do it anyway?
engineerrob1 4 months ago
shouldnt that be a -2 when you take dy/dx of (1/(1-2x))
BIGBobJohn23 4 months ago
Patrick...How do we go about finding the first few coefficients for a power series...
i.e.
c0
c1
c2
c3
etc...
jaredhill823 4 months ago
really wish i found these earlier!
natecc 7 months ago
post more examples plz! thanks for everything!!!
pukhtunpride 7 months ago
corroborate with Sal and Bill Gates, you guys not only can, but WILL change the world.
runback1983 7 months ago 2
@runback1983 ha, i dont think bill gates is sitting around waiting for me to call : ) but thanks for the encouragement!
patrickJMT 5 months ago
@patrickJMT We would support you in this endeavour!
scilabo 5 months ago
@scilabo ok, go tell them! not much i can do about it
patrickJMT 4 months ago
@patrickJMT I've been watching Khan Academy for the last few months. You really picked up where he left off in the Calculus series. I'm totally a Patrick JMT convert and tell everyone in my calc class about it. I really think if you were to collaborate, it would take the educational community by storm. Thank you for all you do here! I will definitely donate to the cause as soon as I'm not a terribly poor college student!
mytwohands 4 months ago
@mytwohands thanks for spreading the word : ) i have emailed him but i do not think he is interested : )
patrickJMT 4 months ago
@patrickJMT That's a shame. Maybe he is happy how he is now with his big pay check from M$
krzysiekz91 3 months ago
@mytwohands epic. i love Sals videos. Ive survived engineering school
xE4syComp4nyx 3 months ago
@patrickJMT You were there for us in some of our darkest and most desperate times of need. You are helping future scientists, doctors, engineers(me), and mathematicians. These are the people who are going to be forging a better path for humanity. You are helping mankind progress and the world will be better for it. Thank you Patrick.
conglacious 3 months ago
Uh,this one was really hard :P Had to watch it like 3 times but finally i got it ^^
MeSooCrazyy 9 months ago
Thanks for the video. That was pretty cool seeing how you could manipulate a function to get the power series representation. It probably does take more examples to get used to it, and I'm all for more seeing more examples.
GohansRiceBall 9 months ago
the phone call and caterines phone number distracted me... cant focus anymore.
SkinnyModelAysa 9 months ago
i see what you did at 3:00, you differentiated the summation itself. what we were taught to do was, write out a few terms of the series, differentiate each, and find a pattern so you can write it in general form.
SGvince22 10 months ago
Excellent videos man! Like many others I'm stuck teaching myself because my actual professor, and I use that term loosely, is useless. Thanks to you, and others like you, I'm actually making sense of this stuff. So thanks again, and if possible I wouldn't mind seeing some more examples on this subject. Cheers!
jasonjkeller79 10 months ago
Educator.com, my ass!
21wakko12 10 months ago 2
just want to let you know that i love all your videos! thank you so much!
But I've never been this lost in my entire life! when do you integrate it and when do you differentiate it?
or how do you know which one to do? thanks
iqbalb619 10 months ago
Haha i looked at my phone when i heard yours ring.
schustar322 10 months ago
Why didn't you pick up the phone? I just wanted to say how awesome your videos are!
TCrunningman 10 months ago 2
Some needy Calculus student on the phone, sounds like.......
loojiji 10 months ago
was that Cathron calling you :P
imkaneforever 10 months ago 13
@imkaneforever lol i think it said cathreen unless it was his robot girlfriend...
Cathreen + tron = Cathron. :O
wellitstrue102 10 months ago
lol i saw the number even tho you tried to hide it
crossxfuse 10 months ago
I still dont understand when to start the series at 1 or 0.
mikegovikes 10 months ago
@mikegovikes try writing out the series for the first few terms and see where ur differentiated/integrated series begin
Bill10N 10 months ago
@mikegovikes
I think that when you derive a series that starts at 0, you need to start at 1 instead of 0 for "n" in order to start the series off with a constant
SnareStyle10 10 months ago
I love you so much <3
Omlit 10 months ago
I'm havin a hard time understanding the concept
paki123 11 months ago
derive the power series for g(x) = (1+ X^3) ^(1/2) and put into sigma notation i need help on this problem
rlyconfuzd1 11 months ago
THANK YOUUUUUUUuuuuuuuuuuuuuuuuuuuuuuuUuuuuuuu
Bosskane 11 months ago
Hey, for the second question you did; what if you got c to equal a number.. then if you subracted it from the equation you got to make it look like the original question it wouldn't be a power series anymore right? so what would you do? and btw thanks so much patrick for providing us with so much help.. it means a lot to me and everyone else.
floyd617 11 months ago
Just wondering... do you know when to change the n values? like n=0? n=1? when to change it? because I have no idea when to change it..
StarVans 11 months ago
would love to see more examples of all types of series
nike9107 11 months ago
U're right! u might have to take a look at the video a couple time to understand :)
khanhishere 11 months ago
Comment removed
enwyookee14 11 months ago
hey Patrick, I really wish you would've done a easier example before this one.
1230lilyjune 11 months ago
Hi great videos, As of last week I started studying "sequences and series". Again, the branding chosen inappropriate and unnecessarily confusing , not distinguishable at all. I would leave "sequences" as it is but would refer to "series" as "add-series" or better yet "add-sequence or sum-sequence" simply because now, in the word the clue of summation already has been giving in the initial descriptive sense.
enjoyablesounds 11 months ago
how can I find the radius of convergence? I'm confused.
abthurd 1 year ago
@abthurd you should watch the video about: radius of convergence
patrickJMT 1 year ago 15
you're such a great help, dude.
God bless.
FroMaestro 1 year ago
Thank you so much for connecting the dots that the calc book doesn't.
patricktification 1 year ago
Please do more examples, this is pretty next level compared to the other stuff
zoom2121 1 year ago
How do you know when you should differentiate and when you should integrate? What do you look for in the problem?
ChesterELbajista 1 year ago
DId you go answer the phone? LOL that was funny!
ChesterELbajista 1 year ago
Hi thanks for the vid. A question though. Why dont you shift the index by replacing n with n-1 in integration, much like how you replace n by n+1 in differentiation?
Thanks in advance
DieNo0b 1 year ago
Dude you are awesome
bdmleo1 1 year ago
thanks for your videos!!! they really helped me out!
ecgimenez 1 year ago
wow this is intense o.o
honeypot11 1 year ago
i've been watching all of your calculus videos since my midterm, since then my grade has gone up TWO LETTER GRADES. Tomorrow morning is my calculus 2 final and if i make an A on it i make an A on the course. i dont wanna jinx myself but ive been studying like crazy with the help of your videos so i feel good. If i get an A i will donate my life savings to you and name my first child patrick. no lies.
peslie25 1 year ago 4
@peslie25 ...even if its a girl?
kh0t9 1 year ago
Could you please do a few more examples? :)
picacura 1 year ago
I don't quite understand why 2^n inside the sum is treated as a constant...doesn't it change with each term? Isn't x really the constant here?
Jawshooah 1 year ago 2
@Jawshooah it is a function of x.
patrickJMT 1 year ago
@Jawshooah to be more specific, it is on respects to x
aznelf13 1 year ago
@Jawshooah I was going to ask the same thing. I really couldn't understand how 2^n was a constant as well. But I guess since we're taking the derivative with respect to x, that would truly make 2^n a constant. Otherwise, if x was the constant, the derivative of x^n would not be nx^(n-1) but x^n*ln(x).
alphalop 7 months ago
wouldn't that series diverge?
Meex1989 1 year ago
i need help; with a sine and cosine to represent them as a infinte sum.
Forman6 1 year ago
Ok, this is starting to make sense.
FaiththeHairstylist 1 year ago
you've been helping me ace my calc quizzes every week with your clear examples and easy to understand explanations! THANK YOU SO MUCH!!
curbsidelexi 1 year ago 2
@curbsidelexi no prob, keep up the good work
patrickJMT 1 year ago 2
I have a question, how do you know when to differentiate and when to integrate?
I noticed you integrated for the inverse tan function, but then integrated for the other.
how do you know?
tal105 1 year ago
Wait.. So, Patrick. You're saying you started out with Pre-calc in your sophomore year, of COLLEGE?? Dude.. I've been taking calc since my sophomore year of HS and it still intimidates the hell outta me. Your videos help to clear a lot of it up though. Thanks!
iYoungJ89 1 year ago
@iYoungJ89 yes, i believe it was my sophomore year (actually, it may have been the summer between freshman and sophomore year). but i came to math relatively late in life i think
patrickJMT 1 year ago 2
hey patrick.!
I was just wondering what happens when you find the value of C, where would C be, on the right hand or left hand side of the equation?
thank you for the video, it super duper helps!!! :)
aeroj 1 year ago
Thank you so much for putting up these videos, as a freshman in college in calc two with a test on Monday, I really appreciate your explanations of series. You're the best!!
zenaidadg 1 year ago
please more examples!!
KAZAKHTAR777ALGA 1 year ago
Need more examples on differentiating power series!!! thanks.
KAZAKHTAR777ALGA 1 year ago
THANK YOU! I have a Cal 2 test tomorrow and this along with ratio test was so confusing in the book. Your explanations were crystal clear
omgitswes32 1 year ago
You saved my life man, my parents wouldn't let me play Starcraft 2 because i couldn't do my homework on this. Thanks to you I was able to complete my homework and now I can play Starcraft. You are the best ever!
sykku 1 year ago
hey... Patrick in your second problem Shouldn't your C be in the right side of the integral....
well, Thanks for the videos...
geovaniluna 1 year ago
2:40 s something, shouldn't the derivative of 2^n = 2^n.ln2?
raiden233 1 year ago
@raiden233
yes but he is Taking the Derivative with Respect to X.
And when Integrating you integrated Also With Respect to X (dx)..
geovaniluna 1 year ago
ommmmgggg wtf was that?!?!?! All that was just like.....woooaaaaahhhhhh, so crazy. I didn't understand what my professor was talking about when he did this lecture this morning. But after watching this, I actually kind of understand it now : D. I just have to watch this a couple of more times to fully understand everything. Thank you for making everything much simpler to understand!
Link64 1 year ago
Patrick! Could you explain more why you make the n=1 at 2:39?
I still don't understand why you had to change it from n=0 to n=1.
THX!
whoru206 1 year ago
do you have a lesson about the matrix inverse? The Gauss-Jordan Method?
ronijun888 1 year ago
Patrick! What can I say, man, except you rock! I am taking an online calc II course with very little contact with the instructor but need to the course to get into my grad school that starts in sept. I would, without a doubt, be miserably failing this course without all your videos. You shine light in dark places, bro. Much appreciated!
steelblue831 1 year ago
@steelblue831 i would have failed this class if i had to do it online : ) so keep up the hard work!
patrickJMT 1 year ago
thanx u r the man
MrAbosul6an 1 year ago
Great video! Thanks so much for all your help!
carlampp68 1 year ago
This video is the best! Thanks so much for all your help!
carlampp68 1 year ago
hey man, you the bomb! great work teaching this stuff.
ryezizzle 1 year ago
this is the first topic in calc so far really tripped me up. thanks for all the time you spent on this chapter
janitarjanitar 1 year ago
my exam is tmmrw, can u write it for me?
KosovoJeSRBIJA 1 year ago
if you integrate the original f(x) then find a power series representation for the integral of f then differentiate that power series you should get the same answer?
Jirgo101 1 year ago
hey i really love your videos! is it possible to do one on using a power series to approximate a definite integral to decimal places? thank you!!!
thyballoons 1 year ago
marry me
kottonkandy617 1 year ago
click his ads!!!
mahtab840 1 year ago
@mahtab840 what ads?
Pharatos666 1 year ago
why at 4:18 did you do that multiplication. where did the two's come from?
slipcock21 1 year ago
I'm sorry but I still don't understand what happens with the plus C after you integrate..how DID you managed to get rid of it? From the video, it seemed as though you took an arbitrary value of x and solved for C at that point..sorry if this doesn't make sense..I just want to know what happened with that +C after integration and how to approach similar situations in questions
disc33 1 year ago
this was unbelievably helpful, thanks
youweichen 2 years ago
my school is absolutly not preparing me for college...especially in calc...what happens if I screw up in college bc of a lack of knowing calc before I get to college?
YBPhotoeditor06 2 years ago
well, you, like many others, will have to either retake it, or taking some to prepare you for the class.
this was the same sh*t hole i was in... my school was a total joke. i skipped about 50% of my days as a high school senior but still made A's in everything.
i had to start with precal myself in college (sophomore year)...
patrickJMT 2 years ago 16
@patrickJMT I am studying to become a math instructor. What would make calculus better in a classroom? Although I have an excellent professor, I do most of my learning on my own and with the great help of your videos.
TheXsnipexx 9 months ago
Comment removed
TheXsnipexx 9 months ago
@YBPhotoeditor06 You can always go to a junior college to do generals(it's convenient bc its cheaper) and in 3 semesters(algebra, trigonometry, calculus 1), you can be good to go in calculus 2, 3, linear algebra, ode, proofs, etc.
Axelich 2 years ago
@YBPhotoeditor06 dont worry about it. i didnt take calc in high school, i didnt even take math my senior year. i made an A in calc1 at LSU. although i studied my ass off . it just takes a lot of work, but you can do it
WeDontClem 1 year ago
@YBPhotoeditor06 Your not prepared for college until about a month in. lol. don't stress.
slipcock21 1 year ago
why was there a random annotations box with x's at 2:20
did you do something wrong that i didn't notice?
unknownlove19 2 years ago
i have no clue why those are there... (or were therE, cause i just removed them).
thanks!
patrickJMT 2 years ago
thanks
wujiahunter 2 years ago
the proof of differentiation of power series and Abel's Theorem are very interesting too.
pitelis 2 years ago
LOL it'd be funny if you picked up your cell phone while doing the video
mranderson987 2 years ago
thanks man appreciate it
pimpsta999 2 years ago
Please do more examples!!!!
typeInLIV 2 years ago 24
@typeInLIV can you ask him in a more polite manner? -_-
t3nd10usx 1 year ago
@t3nd10usx Hmmm.... Notice the PLEASE at the beginning of my request. Let's define please. Please: used in making polite requests and in pleading, asking for a favour, etc. Example: "please pay attention" So, PLEASE go somewhere w/ that.
typeInLIV 1 year ago 3
can you do examples of finding the radius of convergence after doing differentiating and integrating power series? Thanks.
unrealriot 2 years ago
for the problem in which you differentiated 1/(1-2x), how would you find the radius of convergence of that? Is it just one? I'm doing my math homework now and I had a very similar problem however, it was telling me that the radius of convergence was not one.
bahstanchyeah 2 years ago
How and where did dividing x^2 by 2 come about?
bobadilla351 2 years ago 2
darn your left-handedness!
but you're still great!
thanks for all the help.
you're better than any tutor.
:)
katiexxlove 2 years ago
can you do more examples of differentiating and integrating power series?
aleyshachara 2 years ago
can you write x^2 / (1-2x)^2 as
(x^2 / (1-2x)) * ( 1 / (1-2x))
then just write it as a power series and differentiate
mdogboy0 2 years ago
thank you so much. my calc 2 professor isnt the best and the book doesnt explain anything. you have helped me a great deal
bfruss0 2 years ago
Why is it that when you differentiate a series the index of summation increases by one, but when you integrate a series the index of summation does not change?
EB30775 2 years ago
well, it depends.
expand out the series expansion, differentiate, and put it back together and you will see
patrickJMT 2 years ago
yo patrickJMT, that was indeed a gr8 help for my finals, thnx a ton man. I needed this help bcz I missed the class for this lecture and this tutorial saved my time , thnx a ton once again.
sharjah12345 2 years ago
in first example if you plug in x=1 - the series will not converge. i think you should have said that the representation is good only in some region.
UuvuOravanLuu 2 years ago
yes, you are correct, i should have emphasized this.
when i made the video, i was focused on the mechanics of the problem
patrickJMT 2 years ago
yes, you are correct that i should have emphasized this.
i was focused on the mechanics when i made the problem.
i also made this video for a student that i was tutoring at the time, and she was aware of the interval, so i did not think so much about it : )
patrickJMT 2 years ago
still your video is very good. and i see you are lefthander, jist like me)
UuvuOravanLuu 2 years ago
In another video you made, you explained that abs(x)<1 is essential for convergence to occur
michaelyo 2 years ago
nvm
kyle5555 2 years ago
i think you did this one wrong....when you take out the (-2x)^2 you keep it as (-4x^2) but it should be (-2)^2 * x^2 giving +4x^2 so the (-1)^n shouldnt be there....correct me if im wrong...
kyle5555 2 years ago
Man patrickJMT... the way you simplified that last problem... I would've never thought of that...thx a lot for your vids..
karama8484 2 years ago
sorry again about the previous post. im stupid. but im confused about the constant part and why that makes it start and n=1 instead of 0
wtmmj 2 years ago
I think it is because if you write out the series before the derivative is taken you'll see a constant at the front. when you take the derivative of a couple terms, it'll still have a constant and to you have to set the series notation for the derivative to start with a constant so that they agree...I think...you should wait for confirmation of others.
karama8484 2 years ago
Question, Why is the derivative of 1/1-2x become 2/(1-2x)^2? I took the derivative to be -1/(1-2x)^2
mustangdale2001 2 years ago
Solid.
NetDialect 2 years ago
Best. Teacher. Ever.
gibberishowns 2 years ago
Why does my instructor make this so complicated?!? Why can't they just show me examples like this? It's not like your making this easier than it really is, because I've been doing 95% on my tests based on these videos.
WiteTlger 2 years ago 2
glad that i have been able to help you : )
patrickJMT 2 years ago
Regarding changing the index, it has to do with the fact that if you differentiate a constant, it becomes 0. So the first term is gone, so you change the index to reflect that. As for the radius of convergence, all power series converge at x=c if they converge at all. Since c=0, in this case, he is using that. The important part here is simply that he needed one point to solve for C. You can use any point, I believe, and it should work. 0 is just the easiest in this case.
sevandyk 2 years ago
The most enthusiastic teacher I've ever seen. You turned off your phone, which rang during the seminar to keep it going. Even my passionate teacher doesn't do that. PATRICK JMT ROX!!!!!!!!!
Anyway, how do we show that S(1/n) (summation of 1/n as n goes from 1 to infinity) diverges extremely slowly? We can't do it using Test for Divergence.
chopinandliszt 2 years ago
well, you can show it diverges through an arithmetic argument; to show that it diverges 'slowly'... what does 'slowly' mean? i agree.... if you add up terms... lots and lots and lots and lots of them, you still getting a pretty small number
patrickJMT 2 years ago
your video is great/ I wish you were my calc teacher!!!!!!!!!!!! you should definitely think of moving to Illinois and teach math here!!! *around 2:50 I am kind of confused too D: can anyone explain why he changes the index 0 to 1? D: *
lifeisawesomeXD 2 years ago
I am a little confused... I have seen this a couple times so obviously I am missing something... you say that the derivative of 1/(1-2x)=2'/(1-2x)^2 now... wouldn't you use the quotient rule? 1'(1-2x)- haha nevermind
runnerman89 2 years ago
My brain melted a little, but I think I'm getting the hang of this now.
Weresquid 3 years ago
this part can be a bit tricky
patrickJMT 3 years ago
you are left handed (me too)
Glitchors 3 years ago
I think it's self explanitary. :[)
RageRater 3 years ago
Your videos have helped me so much. I'm a freshman in high school and have just taken the calculus placement exam and it was easy thanks to your help! I'm still very nervous because I'm waiting for the results.
tom92373 3 years ago
cutedude22: Nope, it's clarinet lessons.
colonelmatterson 3 years ago 4
answer the phone!
colonelmatterson 3 years ago
thaaaaaaaaaaaaaaaaaaaaaaaanks
sayeqalkaher 3 years ago
i think im in love...
haveaherbert 3 years ago
who with?!
patrickJMT 3 years ago
for the 2nd prob, it could be a little easier if you substitute u=2x and then plug it at the very end right?
razberrymonster 3 years ago
hey i was just wondering do ya ave any vid sshowing how to do the recurrence relation?
noelmcgrath1989 3 years ago