im glad you fixed the 1/3 at the end, i was trippin balls

Patrick JMT: The reason you haven't switched to business yet.

patrickJMT, you da real MVP

I have my third Calc2 exam tomorrow that I need to get around a 70 on to still have the possibility to pass the class with a C (im a math major, sadly had a bad start this semester) and your videos make this stuff, along with other stuff like the Power series, very easy to learn. THANK YOU SO MUCH!

I am seriously doing great in my Calculus class because of your videos. Your videos help me a lot in understanding the concept! Thank you so much!

OMER SALEEM The difference between taylor and maclaurin is that when a=0 it is considered a maclaurin series. The process is exactly the same however. Hope this helps!

No lie, test in 26 min, been staring at the book trying to understand Taylor and Maclaurin Series. Then I remembered there is a guy on youtube that teaches it very clearly. Bam. 10min later I actually get what I have been trying to understand for hours. Good stuff.

you're the reason why I'm still in college

Patrick...you deserve a fields medal for the proof that math can become lucid with excellent teaching!

Your videos are making my studying for my final so much easier! Your videos are helping me more than my professor has all semester! Thank you so much!

So on all of Patrick's vids, i get ads for Math help, but they are wasting their money by putting their ads before Patrick's videos because Patrick's stuff is so goo already, and it's free. way to go!

@JuniusFaction you are taking it right now as i type this!! i am projecting math thoughts throughout the cosmos... i hope you are getting them!

@patrickJMT i dont mind the ads at all. what you do is phenomenal and provides a perfect addition to working with a textbook. keep up the amazingness that is these videos.

You are like a mother to me all the way from South Africa-Even my pet Lion can do maths now

Patrick JMT: "Sorry i was thinking there for a second" Please you deserve it man, the Real OG

I am an university student from Hong Kong. I just discovered your video right before my maths exam and it helps a lot. Thanks so much!

I hope that you're getting paid for these videos, because you have helped me on so many math assignments / tests over the years. Much thanks my friend!

I seriously watched all you series and sequence videos for this exam tomorrow. I love you. You go slow but i still have to pause it sometimes, and you go over it in concepts so its super easy. This is better than a book. PS im a lefty too *high five*

I've been watching your series videos a lot recently, and I just wanted to say I love your summation sign. It is beautiful.

this is perfect. you have really brought something really complicated and simplified it down in easy steps. you can apply this problem solving technique to anything. any difficult math, science, or any problem rather that you may face, just try to simplify it into easier steps. don't overreact, just take some time, work the problem out, and practice at it. well done

Damn dude. Your my hero. Thanks for these videos. I recently discovered them and I would be clueless on how to do all this without them. Most teachers have no idea how to actually break down ideas into simplistic form so one can actually pick up on what exactly is going on like you do.

I always come back to your videos Patrick. I still don't like math, but I like how you teach it. Thank you so much, honestly.

What a boss, still helping people 11 years later

you have no idea just how grateful i am for your video. Ive been searching all over the place for a good description for a taylor/maclourian series video and my book is no help. you are the first to explain it out so i could easily understand it. +1 subscriber

you make calculus different ,,, im doing very well in my exams just because of your videos , thank you

Your details in all of your calc videos have really helped. There just isn't enough time in class for the teacher to be this detailed. It is nice to be able to stop the video and take notes, etc. Thank you.

OH patrick patrick, my teacher has 20 years of teaching experience, a phd and gives lectures in math conventions in Japan and China. What he told us in 70 minutes cannot match your 10 minute videos. Your pace is so smooth and every step is fully explained which is simply FABULOUS. I am speechless because just 30 minutes ago, I was having doubts about passing this next exam! :DDDDDDDDDD

Signed up for the BC Exam when I'm taking AB. Attempting to learn this stuff in a day. You are saving me man, SAVING ME.

I have a calc 2 for engineers exam in a few days, I have learned more from your videos than i have from hours of lecture and studying.

Knowing how smart you have made yourself without any ap classes gives me hope for myself,that i still might make something of myself in this world today!

Hello, I just want to thank you for these amazing videos! Without them I wouldn't have passed my Math subjects in college. Kudos! :D

I have a test today and until now I didn't understand this stuff. I think it's really great what you're doing and all the people you're helping. Keep it up!

You seriously saved my butt. My calc 2 final is in about 20mins and I was up studying the Taylor series until 4am. Thank you so muchI have to make sure I subscribe!!

I was really depressed when i couldnt know why you had (1/3) instead of (1/2) when a=2, and at the end of the video i was really happy when you fixed it , because I would of changed my major from math to something that doesn't has math in it, or at least has easy stuff... thank u very much and I hope u continue doing these great videos for the students and hope that we can do something in return for all of the great videos that u have uploaded online

@patrickJMT in my case all the software that would follow me for eons if you hadn't help first year computer engineer. You should get a medal.

You helped me get an A in Calc 2 two semesters ago. Now I'm back, refreshing for differential equations. Thank you patrickJMT

Best explanation on the subject I've seen. Much better than how it was covered in my calculus 2 class.. Great Work!

You do your math in sharpie.... ARE YOU SOME SORT OF GOD?!

This semester I had a terrible teacher. Pretty much had to teach myself calc 2 and all thanks to you i passed the class with a low A. Looking forward to your videos for future math classes. Thank you!

I have a test on this stuff in two days. Since I don't understand my teacher, you're vids are saving me. Thanks much!

wow your videos are amazing! i learn more from your 6-10min than i do in my hr and 15min calculus lectures :)

@90sideways well, all the basic laws of newtonian physics can be described as differential equations; power series are a huge way of solving tons of differential equations - so that is one very practical example. also, the 'bell curve' or normal curve in probability uses a function to find areas that can not be integrated using elementary antiderivatives; a power series approximation helps in the area as well. however, i have also not used it yet today in my personal life if that is what u mean

Thanks. My textbook and prof both gave very basic examples that didn't give enough scope to the subject. After watching your video I was quickly able to finish the assignment.

You're awesome. Thank you for taking the time to make these videos and giving them out for free!

Clear, concise and simplicity is always a winner........... keep it up your vids are helping me so much.

Words can't describe how much I love you right now, thank you so much!

An Infinite Series of Thanks! You caught that little error at the end. The rest is beautifully laid out. Pretty amazing stuff, Taylor Series!

I make a mistake when I evaluate the third derivative! I write down 2(1/3)^3 but it should be 2(1/2)^3!!!! I catch the mistake but not til the end of the video, so just be aware of that while watching! Sorry for the confusion!!

excellent! that is a solid return for only 20 minutes worth of vids : )

Your series videos just bumped my final exam up from what would've been a C or D now to at least a B. If the future of this country is smarter and wiser than past generations, you can pat yourself on the back for that.

I learned something this year.... 5 AP classes with AP Stat, BC calc, and Phys II C is insane :o.... Thanks for helping me so much in my worst of the 3. Solid B averages in Phys and Stat but only pulling a C in Calc... Thank god for your vids...

you make calculus so much easier. I learned more from your 10 min videos than from my 2 hour lectures. my professor know his stuff but he bores me to death. thanks. I am learning this for my final on wed

in 500 years humanity will look back and recognize that you existed as the best maths tutor of the century

I fucking love you!!!!!!!!! I was stuck on this hw problem for an hour and then decided to try youtube and bam found this video, ugh never fail Patrick!

in 10 minutes I got something that my professor tried to convey over 3 - 50 minute lectures... and... I am writing this 7 hours before my final, really glad you made these videos. I graduate friday! good by undergrad!

Thanks for your tutorials, they are very helpful. You really summarized 2 hours worth of lecture in under 10 minutes.

Thank you so much!! You make it so much easier for me to understand. I'm sure you have helped thousands of students across the world.

your sum-sign (sigma) looks like its written in Metallica-font.

this lesson alone was more important than my 4 months in the class kudos Mr...

So much better than the BS notes my school gave me.

Great video man. I love the way u just explained whereas my teacher, She doesn't know how to explain. I am subscribing to u.

yes, as pointed out in the annotations and in 1000 other comments below, including mine. not sure what else i can do to make people aware of it. if u watch the video, i catch the mistake. thanks tho

dude keep doing what you are doing. u rock. way better than my college professor

Damn. I got my midterm exam in2 days , and youtube just reminds me about this video after 13 years. Love it.

I see I'm not the only one watching these vids before finals week! Haha........good luck to all of you, and may PatrickJMT save us :) !!!!!!

thanks so much!!! i spent a whole hour trying to figure out a problem and i got it shortly after watching both of your videos.

lol. Those two 3's that appeared there were torturing me till the very end until you caught them. This video really was awesome! Thanks a bunch!!

at the third derivative you put (1/3)^3 instead of (1/2)^3 ..thanks for all your vids by the way...you're a life saver.

man if i had found these videos a few months before i would have passed both of my exams...good job these are really helpful! :)

The ads asking me if im tired of youtube tutoring videos on a patrickjmt video are hilarious.

Thanks patrick, you go though these examples at the perfect speed.

than you should finish watching the video before saying stupid comments because he corrects himself at the end.. dont listen to people like this @patrickJMT you are doing a great job

One of the best MTH professors ever!!!!!!!!!!

U just did the exact problem I was stuck on. I love u so much right now.

sometimes, when im doing problems, i put on your videos just to hear the sound of your voice and it helps me concentrate...hahaha but seriously dude thank you so much, finally done with cal 1 and 2 and your videos helped loads :)

for the first two years, i put these up 100% for free, with no intent or promise on getting anything in return (this is one of those videos). now the partner program does pay me, but that is certainly not why i started.

These tutorials are worth watching repeatedly.

thanks patrick! I've been following your videos for my calculus exams since last year and they've helped me do very well! :)

Thanks a million Patrick. I enjoy watching your videos even for the topics I know

thank you so much for your videos! my textbook doesn't explain calculus nearly as concisely or simply as you do. you're the best!

thanks for saving me from wasting money on a course i could have failed, good guy

Very helpful, my calculus teacher assumes we know what is happening and why we are doing it. This helps me a lot thanks!

@snakegaer you are very welcome

@aniyeats glad you like them! : )

the idea is that a taylor polynomial of degree n approximates the function f(x). suppose that you wanted to use the taylor polynomial to approximate f(2.1)... by centering the taylor polynomial at a=2, your estimate will be closer to the correct value as opposed to say, centering the taylor polynomial at a = 10. basically, the taylor polynomial provides 'good' estimates for those values of x near your a value. so, if you need to calculate f(1000.5), you would use a = 1000 instead of a = 7, etc

@aesrp used to teach college but not any more. to teach at a university ( a decent one at least) you have to do tons of research typically (no one cares if you can actually teach); i am not so interested in 'publish or perish' so i bailed out on my phd program. i still taught for a while, but i found i was enjoying it less and less so i stopped.

Thanks a lot for all the videos! I'm a first year industrial engineer student at GroupT and your videos really help me out on stuff I don't quite get :)

@patrickJMT So true about profs not needing to know how to teach. Our calculus class is being taught periodically by a woman who nobody can make head nor tail of what she's trying to get at. She went through an hour lecture which I figured out was suppose to be teaching Taylor Series and never once mentioned "Taylor series" as it's title.

Just took AP BC test today, I'm not exactly sure how I did overall, but I completed series questions perfectly thanks to you. I'll know when the scores come out for sure though!

Anyone else notice Patrick your voice sounds so much deeper in these older videos? Thanks for the help PJMT

@DTSchey09 thanks for the kind words :)

@FaiththeHairstylist eh, not the end of the world. i put in annotations and correct it at the end, so... it happens : ) i do remake videos where the mistakes are 'more severe'

You rock man. Got a final in few minutes and you saved me! Keep on trucking bro

@patrickJMT my exam goes well.. im really confident to take the exam because i know i reviewed... and that's because of u..thanks again mr! :)

wow patrick great moves! keep it up proud of you!

@Metalgod89 the ads are how i am now able to get a small financial reward for my videos. it means i can now spend more time making them!

Patrick, thank you! You are rocking it out -- I have finally grasped this concept because of your video!

Hey Patrick, thanks for sharing your knowledge free of charge, really convenient for some people's budgets like mine! who are eager to learn :))

I was stressing out over my final tomorrow that has this on it but now I think I will be able to do it! Thx! This video is excelent!

Patrick, you are a saint, thanks for all these videos