❖ Power Series Representation of Functions ❖

[@muse778899]

Hey Patrick, Just wanted to say thanks for all that you do. I started watching your videos back in high school...they were so helpful back then! Then I went to UNL where I got my BS in mechanical engineering...I constantly referred to your videos then. Now I'm at Yale getting my PhD in mechanical engineering, and here I am, watching your videos! Seriously, you have an extremely concise way of explaining things. If I ever want a refresher on a math topic, I come to you first! It's weird, you are like the best math teacher I never had. Keep it up! Cheers, Walter

[@patrickjmt]

+Walter Bircher awesome! if you are getting a phd at Yale, I should be watching your videos! im flattered and appreciate your kind comments.

[@abdulkadiryilmaz4085]

hey Patrick, I'm studying mechanical engineering too and I still watch your videos for calculus 2. I hope I will make a comment on your videos, like Walter, when I will study in Ph.D. for mechanical engineering

[@Ahmed-ny1xc]

@@abdulkadiryilmaz4085 did you graduate yet?

[@abdulkadiryilmaz4085]

@@Ahmed-ny1xc wow, time flies.. right now I'm at my senior year, hope to comment when my school is finished :)

[@Ahmed-ny1xc]

@@abdulkadiryilmaz4085 I'm currently on my sophomore year of Mechanical and Aerospace engineering. Good luck mate, you'll do great, Salam.

[@carllemieux9893]

It's crazy because every 5 to 6 months (ish), new semesters are starting and you change more and more people's life. Keep it up, you have no idea how much of an impact you have on people all around the world. You just saved me, in 10 minutes, at least 4 hours of busting my mind trying to understand what my teacher failed to teach me. Thanks again.

[@Destrxx]

Now I go to lecture to find out what my professors want me to learn and then watch your videos so I can actually learn the material. Thanks so much!

[@patrickjmt]

Happy to help!

[@ISLAMguidanceful]

+Peanutbuterjelly lmaoo i got an A in calc 2 and the professor thought it was because of her XD meanwhile this man teaches me everything.

[@Fikayoz]

+Peanutbuterjelly Me in a nutshell. Goes to class for 2 hours: Understands nothing. Watches Patrick for 10 minutes: "Oh! So that's how that works!"

[@James-cq9dp]

Patrick, Dude i have been watching your videos for math help since high school math.. i am now in college taking calculus 2 and still watch your videos.. You have helped me so much. THANK YOU for being so awesome.

[@patrickjmt]

my pleasure!

[@DoItLive03]

once I graduate college and get out of debt I'm donating to this math jesus

[@MyIzzu1]

DoItLive03 Have you completed your promise

[@Toroidal_Vortex]

Mizu Izzu Maybe they never graduated or got out of debt?

[@Mercurymarvin]

so never

[@luiscisneros8694]

This guy never got out of debt, RIP

[@muhammadm241]

DoItLive03 Are you still alive though?

[@amandafang280]

JUST WANTED TO LET YOU KNOW THAT I AM FOREVER GRATEFUL FOR YOU AND YOUR VIDEOS!!!!!!!!!!!!!!!! KEEP DOING U PLZ

[@patrickjmt]

thanks for the kind words. glad i was able to help you out!

[@samarthk4130]

hi Patrick, I'm here fourteen years later after your video's been published, and I can for sure say your teaching style is brilliant and the video is still the simplest yet most comprehensive tutorial of power series on the internet.

[@Austinbarton247]

Studying Civil Engineering at SIUe and literally watch all your videos prior to the test. You Rock hands down, you are a gift from god. THANK YOU!

[@patrickjmt]

glad you like them. i have a sequence / series playlist although there is probably a few videos missing from it

[@dual85]

I'm in Calculus III and I still find myself coming back here! Thanks Patrick for everything you do. Through hard work and your lessons I'm building my future - I couldn't be more grateful.

[@marccrowell9598]

You speak and write so clearly! Way better than my Calc 2 teacher. Keep up the good work!

[@johnnyjohnson6815]

Patrick, I have always been exceptional at math, and I was a Calculus I tutor in high school. Coming to college, I thought Calculus II would be simple for me. I was stuck with a Canadian(French) professor, and I have struggled all semester. You have a clear, organized lesson for each topic of Calculus II, and I learn more from these videos than I do from going to all four hours of lecture and the help sessions every week. Thank you for your time and work in creating these videos!

[@ZidaTheBlazing]

You're awesome man. Every time I'm crunching before a test, I make sure to watch your videos to get another explanation and it's helped my test grades immensely. I like that you have a sense of humor too. Enjoy your champagne, soft bed of cash, and girls.

[@Twittygurl17]

Patrick, all i gotta say is you're AMAZING! i'm just learning this and i swear my professor was high because he rushed through it i lost track of what he was saying...but, you've just enlightened me tonight and i'm grateful! you're the only person whose videos make sense! THANK YOU!

[@StandforTr00th]

You’re so clutch man. Please keep it up. You have no clue how you’re saving people’s lives with these videos

[@jarlhamm]

You're literally the reason I pass my math classes with good grades... as soon as I graduate I'm sending a nice, fat donation your way.

[@danielgrobbelaar9672]

95% of university lecturers would yield a higher pass rate by simply playing Patrick's videos on the projectors in class. Thank you, you're pulling me through my 4th consecutive Engineering Mathematics module.

[@EriNatori_FFXIV]

You have a talent for expressing 50 minutes of lecture into short 10 minute compact videos. Much appreciated.

[@bradleyedlebeck8310]

Patrick, I just wanted to say thank you for all the time that you put into making all of these videos for the sale of helping people out, not only do you cover so many topics, but you explain everything extremely concisely and in a way that is understandable. I hope you understand how much you help everyone out. I am currently taking calc 2 on track to go to medical school and consistently refer your videos to my peers. Thanks and keep up the great work!

[@MikeShen69]

You seriously saved my university career. I don't know how to thank you in a more genuine way.

[@craigslinter]

Hey Patrick, just wanted to thank you for getting me through precalculus, calculus I, and now finally calculus II. I don't know what I would have done without your videos. Just passed my final after another late late night using your videos as a study supplement. If there's anything I don't understand, you always make it simple and painless. Thank you!!!!!!

[@patrickjmt]

happy i could help for so long! :)

[@patrickjmt]

ha, glad you like the videos :) and better than a donation: TELL LOTS OF OTHERS ABOUT THE VIDEOS! ;)

[@Sweet92Devil]

OMG i got an exam on the 14th, and iv'e been praying for a miracle....it's like u fell outta heaven! Thank you!

[@jokermessiah8361]

Love how you repeat the ideas again and again while applying them. Kudos to you sir.

[@sneakers_guy5488]

Now in what looks like my final calculus class of university, I just wanted to say thank you so much for helping me with math ever since grade 9 all the way to second year of university! The amount of homework problems you helped me out through, tests you helped me prepare for, and concepts to help me learn is insane; I just really appreciate all the work you've done for people like me.

[@Lazuli1989]

I've just got to write in and say how wonderful these videos are. My calculus exam is in a just few hours and these lessons have been SO helpful over the past week of studying. After having a teacher who taught us more about *number theory* than calculus, I needed some serious help. Thanks so, so much for these! :D

[@nikolalubbe2708]

You helped me pass most of my subjects! Thank you so much!

[@patrickjmt]

super happy i could help :)

[@Dleger13]

Patrick, i don't want to even think about where my grade would be right now without you. Thank you so much! I'll be sure to spread the word of your videos!

[@Bakugantsuvai1]

We definitely need more examples of these.

[@jashar1]

You are a GOD-SEND! Why can't our calculus books be written by people like you? My book makes no sense at all on this subject, and yet you're video makes it crystal clear. Thank you so, so, so much for the time and effort you put into this video!!!!

[@kandigirl11]

After watching your videos, I have learned more from them than the entire year of College Calculus I and II. Thank you so much! These videos truly are a lifesaver!

[@qaylin]

I just home from a 2 hour lecture on the power series. About half way through I looked around an everyone had stopped writing and just looked extremely confused. I came on here and watch 5:47 seconds of this video and everything makes sense.

[@sohret33]

Hey Patrick! Just wanted to let you know that I passed my Calculus-1 class thanks to you. Now I’m taking Calculus-2 and I’m definitely gonna pass it because of you! Thank you!!

[@dlrion]

I spent two and a half hour's the other day watching your videos. I learned more in that time frame that I did in the last two and a half weeks of class! Thanks so much. You are the reason that I will pass cal II this summer.

[@zelikris]

"Tired of scrounching youtube for math help?" NO! I have Patrick.

[@patrickjmt]

thanks friend for the kind words : ) i am glad you find my work helpful

[@AsiankidPRO]

I definitely shared this with my entire math class. You, sir, saved my grade and life in Calc.

[@patrickjmt]

@Monsterenergy791 when i would teach the 'why' part - everyone would zone out. is this on the test?? they would ask. can we just see the examples then? they would ask. the 'why' part is the complicated part; it is not tested because almost everyone would fail calculus

[@mattf694]

Yo had to tell you thanks man...since i started studying with these vids my calc2 grades have been better than ever..def spreading the word.

[@Sayuridesu]

This was SO helpful. You just made the textbook I am using in class and what the professor was trying to say crystal clear in ten minutes...You're AWESOME.

[@tianhe8388]

you're the only thing getting me through this course haha

[@Hewbrewkid]

yeah thats pretty useful ! knowledge is power !

[@Gunman160000]

Thank you so much for uploading these! my teacher doesn't do a very good job of making sure the class understand the matierials, so she assigns us assloads of problems to do from our textbook to compensate for her lack of teaching.

[@The_WAAAGHSMITH]

Thanks man. A professor sent me here, and I'm very glad he did. I appreciate that you take the time to explain this, which you do so well. Thanks a ton, man.

[@HamzaJaan786]

outstanding! im a cal 2 student at JC. This stuff is amazing man! Clear voice, easy-to-follow explanations, and it is obvious that you have a deep understanding of this material. Thank you!

[@mmka5434]

You deserve to be called a real professor of mathematics! Great explanation! Thanks!

[@omaraljedani4727]

Patrick thanks a lot first. Secondly I really suggest that you put a link under everyone of your videos for anybody that wanna give something back to you like a couple of dollars from here and there so that you keep up on doing the good work that you do on KZbin.

[@jcshumpert]

Thanks... You explained this topic in 10 minutes better than my professor did in an hour and 15 minutes... Thanks again

[@rogerg0834]

Man you are amazing. I can hardly believe that in a 10 min video I can understand what to do where as in a 1hr 40 min class I can not!!. Awesome work!!

[@thearcenist]

wow, thanks man, after 30mins worth of ur vids i understand power series now as opposed to 4hrs worth of lectures at uni.

[@aznsk8ndude911]

This was a big help. I was confused in class today and after just watching this video I clearly understand it. Thanks!!!

[@patrickjmt]

@Monsterenergy791 that is true. that is why professors are doing proofs in the first place. that IS the 'why' part. of course, i think they could make the problem a bit more intuitive first. then the proofs make sense. but math is taught ass backwards - the theory is all taught 'up front' and it is just to confusing/cumbersome if that is the first time you see it.

[@fatal0bazooka]

I got a 95 on my test thanks to your explicit videos about series.Thanks Patrick,you're the man!

[@jayr64]

i know you have heard this many, many times before... but THANK YOU PATRICK!!! you my friend, should be cited as a major reason for me ever getting my degree

[@ra3ekeef521]

I haven't attend to my calculus 1 & 2 classes except in the exams since you're explaining the calculus here by watching your videos.you make the calculus easier than my professors :) Thanks Patrick

[@patrickjmt]

you can center it anywhere you want (so long as that value is in the domain of the function).

[@gibbo1496]

you're great dude...teachers always assume you remember the shit that you learned like 3 years ago and skip steps that you always include which is very helpful

[@CtheKidie]

I finally get the x^(n+1). My professor and students solutions manual didn't explain as clearly as you. Thanks man! Props to you!

[@sw33theart1118]

You should be paid to do this. Thank you so much. I've stopped going to lectures because I just didn't understand my professor and I got an A on my last exam after watching your videos

[@rn85ccrunner]

Patrick thank you so very much you are a true god at explaining things so very well. Everyone one of your videos has been the most imformative clearest explanations ive ever witnessed. Im now looking forward to my calc 2 test tomorrow.

[@ngflowmaster3519]

The way you explain everything in all of your videos is absolutely phenomenal! My professors should take a page from your book.

[@TeenReporter]

If I pass calc 2, you sir will be the only reason why. You explain this in ten minutes, yet my prof can't do it in a week. Thanks a bunch!

[@RakhiMahbuba]

All of your Math videos are unbelievably helpful!

[@EgoWafflez]

You teach this material better than my professor with a doctorate from Yale. THANK YOU SOOO MUCH!!!!

[@therealalphageek]

patrickJMT, did I ever tell you how much I love you? You make a 3 month class seem like a 1 day class ^^. You are saving me right now from loads of stress haha

[@chiemekaisioma1877]

Patrick is great..he has solved 95% of my calc 2 problems

[@psantoro95]

You make this seem so much easier than my teacher. I wish she could just play your videos during class and then answer any questions.

[@CodyLuu]

I have a cal 2 final tomorrow at 8am. this video saved my life. thanks patrick

[@Naked_Snake]

Okay, so if I used my textbook for this, it would've taken up some time and you summarized it in a matter of minutes! Thank You Patrick! You're awesome! Time to start the questions in the text and maybe then I'll look at what the book wants to tell me.

[@winters792]

You just explained something in five minutes that took my teacher an hour. And I actually understood it this time.

[@dalellll]

Oh my god, I didn't understand this until just now; have been struggling with teaching it to myself for a couple of weeks. Seeing it done makes such a difference. Thank-you!

[@Ammaray]

Patrick - Love your videos!! I rely heavily on your tutorials to solidify my understanding of calculus concepts. I recommend them to everyone I know who could use help with math, and I will continue to do so. Yours are the best, hands down. I have a request: Would you mind doing some videos about FINDING A POWER SERIES APPROXIMATION FOR A GIVEN FUNCTION, CENTERED AT X VALUES OTHER THAN 0? If you could, I would be very grateful to you. Keep up the good work!

[@surfsk8smoke]

Funny thing was I needed some help and I was researching on the internet and figured to mess around and see a video on the same topic. Turns out you perfectly answered my problem! Thanks a whole lot! Ohh and I'll get the next round of beers buddy!

[@patrickjmt]

@ParsVid the whole quick lecture? mainly i keep the videos short cause that is what people seem to like

[@yuhoseok47]

Patrick.. You're awesome. Your videos are way better than my professor's lecture.

[@patrickjmt]

if calculus books could talk... : ) glad i have been able to help you - glad you appreciate my efforts (many, many hours!)

[@ahmednajib3376]

Thank you very much .... you are making my college life much easier ....

[@patrickjmt]

this is a geometric series though (in form) so it never converges at the endpoints

[@giantsockmonkey]

WOW thanks! I never understood my professor's lectures and yet you made it sound so easy! THANK YOUUU! :D

[@unanimed1]

Thanks to you I got 102 out of 100 on one of my tests. You're the best

[@utearingmeapartlisa]

your videos are really outstanding a lot of my friends are firm believers in khan academy, and im a fan of his videos too but I find that for my calculus class you are by far my best online resource. thank you so very much

[@JMRolf1]

Sir you are the math messiah. I bow down and worship you.

[@Pater_Robert]

THANKYOU, I didn't understand this. Turns out I skipped a few pages in my book :P I just want to thank you in general, just like many others I receive great help from your videos! You're the best!

[@jsphamoabeng]

I can honestly say this guy has thought me more in my college career than any my bloody professors!!!

[@bubbaliciousish]

your penmanship is so amazing

[@jackstorm777]

You sir, are freaking awesome. Since my Stewart calculus book is a pile of shit and barely uses any examples, you are my savior.

[@kasikachan]

Your videos make Calculus soooo much clearer!!! Thank you for using your time to make these informative and understandable examples. You are an amazing person! ^.^

[@ismekin]

Hi Patrick! Thank you very much! This video has covered my boring/confusing 2hrs lecture in 10mins. Now I am prepared for the quiz tomorrow! I wish there's a physics version of Patrick on youtube, too so i can ace my physics class =D

[@CLG111]

I've watched several videos and yours actually makes sense. They make this stuff difficult for no damn reason. Ummmmkay

[@IluvHKong]

Thanks so much .You're an awesome math teacher.

[@MadeInHK431]

incredibly helpful :) watching 2 of your videos covered the confusion of 2 weeks worth lecture

[@Yatunic]

Got an exam tomorrow and this video finally made the concept click thank you so much.

[@inyangetuk3399]

now this is what I call an explanation. You should be my professor!

[@JaktheAtheist]

You are the best Patrick. You're videos are what let me pass Calculus

[@briella.p]

I'm blown away by how much more ready I feel for my Calc 2 final. :) You're great dude!!!!!

[@patrickjmt]

i hope it goes well!

[@Orab70]

"And now we have this good form". Love it. Thank you so much for your help. Got a B+ in calc II...I shudder to think what may have happened w/o your help.

[@marcuscampbell3366]

Ive been watching your vids Engineering 101 (my freshmen year), if it wasn't for you I don't know what major id be. BUT i plan on donating to you very very soon! You rock!!!! And if it wasn't for you I'd still be doing my homework in pencil, there's something about that sharpie.....

[@ceker03]

Patrick, you are an awesome. My school language is English therefore ı am following here most of my lessons,Greetings from Turkey.

[@patrickjmt]

@maiie5 what numbers squared are less than 1/9? if you are watching a video on power series, i have full faith you can figure that one out : )

[@patrickjmt]

@KByunish in general you have to check them, but here they will be excluded since the original series has | x | < 1