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❖ Integration using U-Substitution ❖ 

patrickJMT
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23 окт 2024

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Комментарии : 1,4 тыс.   
@patrickjmt
@patrickjmt Месяц назад
Hi all! Wanna help a RU-vid education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
@ballerbob388
@ballerbob388 9 лет назад
I have been using your videos for calc 2, cal 2 for life sciences and now calc 3. your videos have persuaded me to add a minor on my major. as long as you keep singing nobody will get tired of dancing.
@patrickjmt
@patrickjmt 9 лет назад
Oh wow, that is literally one of the best comments ever
@pbrayat2404
@pbrayat2404 8 лет назад
so deep, i saw adele rollin'
@pbrayat2404
@pbrayat2404 8 лет назад
so deep, i saw adele rollin'
@linusherr8257
@linusherr8257 8 лет назад
Baller Bob Would one use the substitution method without using the chain rule? As in the last problem?
@jackcabral7354
@jackcabral7354 7 лет назад
Baller Bob I
@robertherrington3379
@robertherrington3379 10 лет назад
When Patrick is explaining a problem. I listen closely. What I hear is the voice of God saving me from my math exams lmfao!
@TJace50
@TJace50 9 лет назад
LMAO
@gilbertoaltamirano4543
@gilbertoaltamirano4543 9 лет назад
You sir, just won the internet.
@rirecvz
@rirecvz 9 лет назад
Robert Herrington LMFAO ! I feel the burn now !
@TheBlackLodger
@TheBlackLodger 6 лет назад
Patrick JMT = the 2nd Coming of Christ. In other words, he's a life/grade saver.
@David-fj2bx
@David-fj2bx 6 лет назад
Good comment
@revit.2184
@revit.2184 11 лет назад
After a 2 hour class, i'm lost... >.< After a 10 minute video, its a piece of cake! You're just awesome!
@sxge4751
@sxge4751 5 лет назад
this still stands today
@TheSouthBeachElites
@TheSouthBeachElites 4 года назад
@@sxge4751 can confirm this is true
@Haza-rp1cb
@Haza-rp1cb Год назад
9 years later we all like this bruh
@asurastorm8566
@asurastorm8566 11 лет назад
Hello Patrick. I'd like to thank you for getting me through my first year of Calculus. Your videos are great and helped me understand just about everything I needed to know. You really should consider making a book. I feel the one I'm using right now does a terrible job in explaining even the simplest of problems. On top of that, the examples they give are incredibly easy and don't give justice to the problems in their section. Once again, thank you.
@nomad6337
@nomad6337 10 лет назад
tell me about it, i have to give an exam and the book isn't helpful at all
@volejcore3933
@volejcore3933 8 лет назад
Ok.The world needs more patrickJMT.
@lasseskoulindstad8047
@lasseskoulindstad8047 8 лет назад
Wow that last example went from 0 to 100 real quick.
@NoChance1909
@NoChance1909 11 лет назад
Why is this 10 min RU-vid video better than the 50 min lecture I just had?!
@jclmoose
@jclmoose 8 лет назад
:/ that moment when a free youtube video is better at teaching than a paid college professor
@naylasantana111
@naylasantana111 8 лет назад
I feel you
@tyler681
@tyler681 8 лет назад
Such is life
@shavuklia7731
@shavuklia7731 7 лет назад
lol i study online mostly. i go to school 30% of the time (only because it's mandatory). learning on stack exchange (online forum for maths) and watching the occasional youtube lecture works much better for me
@ianmanning4062
@ianmanning4062 6 лет назад
I think you mean a low opportunity cost RU-vid video :)
@SmittyKat
@SmittyKat 6 лет назад
If professors didnt talk as fast as Busta Rhymes raps then I wouldnt have trouble keeping up lol
@sleepingpetal
@sleepingpetal 11 лет назад
Have you ever consider writing textbooks? I feel most math book writers try really hard to be as unhelpful as possible.
@ducksoop.x
@ducksoop.x 7 лет назад
Seriously, its like they're trying to fail you.
@hisheartofstone
@hisheartofstone 7 лет назад
TRUE AF
@rozikhan2744
@rozikhan2744 6 лет назад
The thing is alot of the material and test questions are based off the textbooks
@danceartist8203
@danceartist8203 5 лет назад
They always try to be 100% correct, so their notation is super mathematical all the time, which sucks.
@MuffinTessee
@MuffinTessee 10 лет назад
thanks for helping me get a 4 on my AP Calc AB test!!
@LoLIHateMyNameLoL
@LoLIHateMyNameLoL 9 лет назад
I found integrals to be so difficult when I was studying for my exam. Now I finally understand u-subs! thanks :)
@exekiajq
@exekiajq 8 лет назад
Once I get my degree I'm gonna make a huge donation to your channel. I owe you big time.
@patrickjmt
@patrickjmt 8 лет назад
+exekiajq can donate on patreon for as little as $1/month. :)
@OpenPlatformInterests
@OpenPlatformInterests 11 лет назад
failed my first two tests of the semester with a 41 and a 64... i spent my time at the tutoring labs and they didn't work... I then found PatrickJMT on youtube for the 3rd test and managed to pull of not only passing, but actually getting an A on the third test with a 96! I cannot thank you enough for making everything so clear!!!
@fuzzygreen3634
@fuzzygreen3634 11 лет назад
Explained something in 5 minutes that my teacher failed to do in 2 hours... patrick is the best out there
@HoyaSaxaMV
@HoyaSaxaMV 12 лет назад
You accomplished in less than 10 minutes, what took a professor at a top level university an entire week. You truly have a gift. I am so thankful to you for posting these videos.
@stawbe
@stawbe 9 лет назад
fyi: you, past exam papers and red wine are my best friends right now. The 4 of us are grinding day and night for my Calc 2 exam next Friday. Thanks so much for all the help!
@patrickjmt
@patrickjmt 9 лет назад
Grinding with your friends may help keep up the overall moral but I am not sure if that counts as studying
@stawbe
@stawbe 9 лет назад
^^ as long as everyone's happy haha
@thewatcherlollol
@thewatcherlollol 5 лет назад
Are you still happy?
@littlemissmurderer21
@littlemissmurderer21 9 лет назад
Hope my commenting isn't annoying, but really THANK YOU for making videos! You're saving my college self from crying into my textbook which doesn't explain things or have as great of examples as you do. I hope you feel really happy knowing you're making a difference on a future environmental scientist. I don't know if you still even use this channel, I'd check right now but I'm watching videos and learning, but I hope you see this!!!
@_MARS_
@_MARS_ 11 лет назад
THE WAY U MANIPULATED THAT LAST PROBLEM WAS INCREDIBLE AND YET SIMPLE.......U ARE A GENIUS!! CANT SKIP MY LECTURES BCUZ THE GUY GIVES ALOT OF POOP QUIZES.
@PaIadinKnight
@PaIadinKnight 10 лет назад
poop quizzes? xD
@patrickjmt
@patrickjmt 5 лет назад
Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!
@zahraoth8745
@zahraoth8745 5 лет назад
Bro keep that good work up! You are saving are lives!! You are my fav calculus teacher ever!!! ❤️❤️❤️
@EchoEcho-q4r
@EchoEcho-q4r 3 года назад
Is there any to connect with you directly for tutoring and help?
@strongwickarts3294
@strongwickarts3294 3 года назад
Is there any way I can keep in touch with you..or any reference book
@shukri1724
@shukri1724 10 месяцев назад
​@zahraoth8745
@ObsidionDiamond
@ObsidionDiamond 11 лет назад
You seriously have no idea how much your videos have helped me! You have been the difference maker between me passing and failing calculus! Thanks so much dude! :)
@AdvocareAdster
@AdvocareAdster 12 лет назад
I learned how to do this in 3 minutes and 38 seconds thanks to you. Even after going to class and recitation, you explained it better than they ever did. Thank you so much.
@Cmweinburger
@Cmweinburger 11 лет назад
Patrick, you are a life saver. Your teaching style is great!
@Ghostoflc
@Ghostoflc 8 лет назад
Ive been trying to figure this out for hours now. It wasn't until i stumbled upon your video that now everything makes so much more sense. You make it clean and easy to understand. THANK YOU!
@missjennablejen
@missjennablejen 8 лет назад
I should just start watching your videos during class when my professor is lecturing. I've learned more in 10 mins than 50 mins from my professor.
@barbaric37
@barbaric37 13 лет назад
my professor went through this so quickly today and I was confused about the whole du and dx thing and how to utilize them. This definitely cleared it up for me, once again! thank you
@GTiR23
@GTiR23 9 лет назад
Thanks man, helped me a lot. You also have the neatest hand writing I've ever seen from a 'lefty'!
@alekhile2449
@alekhile2449 9 лет назад
it's people like you who make it possible for people like me to pass a calc test with a less than stellar professor. thanks again!
@patrickjmt
@patrickjmt 13 лет назад
@Perulaiz when dividing, you subtract exponents. 1 - 1/4 = 3/4
@SnyderChips07
@SnyderChips07 9 лет назад
You're the best Patrick! You've got me through highschool and now you're getting me through college; thanks for the all the work you've put into your videos all these year.
@ActIgnorant
@ActIgnorant 8 лет назад
I owe my math grade to you
@peyton4048
@peyton4048 8 лет назад
+ActIgnorant same brah
@TheArtunism
@TheArtunism 8 лет назад
When you see Earl and Doom in one comment chain
@dumbchicken1
@dumbchicken1 8 лет назад
you mean first born child
@simply_me7266
@simply_me7266 9 лет назад
Thank you so much for this video!!! It helped me past my final exam for Calculus 1 last semester!! My professor rushed teaching us how to solve integrals, and i didn't understand a thing!! He then he told us it will be in the finals; and that's when I started to panic!! I'm so glad I came across this video before the finals!! It helped a lot!! Now I'm taking Calculus 2 where we go more in depth with integrals and now we are learning how to use U-substitution. I feel like I'm advanced in the class; its awesome and it's all thanks to you!!
@MMAWatch7
@MMAWatch7 8 лет назад
When you got a calc 2 test tomorrow
@patrickjmt
@patrickjmt 8 лет назад
+RogueGOW #problemsfrom1/2alifetimeago
@aaronmason3086
@aaronmason3086 8 лет назад
how did it go!
@MMAWatch7
@MMAWatch7 8 лет назад
Pretty good, but now I got another one Monday on series and sequence >:[. Hbu?
@aaronmason3086
@aaronmason3086 8 лет назад
i got a 93 on my first one, second ones on monday , crossing my fingers.. its gonna be harder
@jhoannajanealberca3642
@jhoannajanealberca3642 8 лет назад
hahaha.. 😂
@noahalexander3607
@noahalexander3607 5 лет назад
I can't even express how thankful I am. My exam isn't till next week but I wouldn't have figured this out if I had not come across your beautiful self.
@maniclokofe4585
@maniclokofe4585 8 лет назад
THIS GUY IS THE BEST! I WISH HE COULD BE MY MATH LECTURE
@dkscidmore
@dkscidmore 11 лет назад
Video made my day. Been working on this stuff for 4 days now, and these videos explain it so much better than my teacher.
@manutd931
@manutd931 11 лет назад
YOU SAVED MY BALLS MAN I LOVE YOU.
@alanwrigglesworth7562
@alanwrigglesworth7562 10 лет назад
our lecturer made it so convoluted i couldn't understand a thing until, once again PatrickJMT became a freaking legend. thank you
@223Warlord
@223Warlord 9 лет назад
so du just falls off the map after integrating?
@kbmagnus12
@kbmagnus12 9 лет назад
+GAO Xiang2 It is just a notation of which variable to integrate. so yes it goes away after integrating
@shaolin_tcg4727
@shaolin_tcg4727 8 лет назад
thanks I was wondering the same
@chrisross9467
@chrisross9467 8 лет назад
kinda like how my dad went to the shops to get some milk but never came back....
@Really_Biggah
@Really_Biggah 5 лет назад
chris ross I’m so sorry to hear that. Hope u ok
@thewatcherlollol
@thewatcherlollol 5 лет назад
@@chrisross9467 it really do be like that big chungus
@KIB840
@KIB840 7 лет назад
You are the best Calculus teacher I know. You make everything so simple and easy to understand. I appreciate you a lot.
@afiacco9155
@afiacco9155 9 лет назад
I am in calc II I just needed a few more of the polynomial. good video your my favorite math teacher. Which is sad lol
@patrickjmt
@patrickjmt 9 лет назад
Thanks, that makes me feel good
@patrickjmt
@patrickjmt 9 лет назад
Thanks, that makes me feel good
@muzicjunky1
@muzicjunky1 13 лет назад
seriously you are a great help. if your not teaching you should write text books. like how to text books with references to your online videos. thank you sooooo very much you are a life saver
@MrBrandybuck1120
@MrBrandybuck1120 9 лет назад
You, sir, deserve the Presidential Medal of Freedom
@auristelabantegui7887
@auristelabantegui7887 7 лет назад
My first calc exam in Uni is in 36 hours and I'm literally just watching all your videos since I started studying! LMAO you are my saviour thanks!
@Horse1083
@Horse1083 9 лет назад
You are awesome! Thank god I found you! Keep up the good work! (Even though this is from 2008 lol)
@Solaris989
@Solaris989 13 лет назад
two weeks of lectures and i couldnt figure out what my professor was doing. 3 minutes here and i understand it, thank you patrick
@david_m157
@david_m157 7 лет назад
They should use his demo's on Mymathlab, who agrees?
@patrickjmt
@patrickjmt 7 лет назад
+David M send them a message and let them know
@david_m157
@david_m157 7 лет назад
Hah, Pearson education may not want good content associated with their name.
@agumonkey
@agumonkey 8 лет назад
So envious of people that write calmly and beautifully like you.
@RedBar3D
@RedBar3D 9 лет назад
I've understood that treating dy/dx as a fraction is a fairly debated and discussed area of mathematics and engineering, even historically. Could someone provide me with an intuitive feel of why treating dy/dx as a fraction is legitimate and why it works? I haven't studied u-substitution or complex differential equations yet, and I wouldn't want to use it without understanding the underlying theory and the underlying proofs. I understand that might be a bit too much to fit into one youtube comment, though. So an intuitive feel for why it works would be great. (alternatively provide me with a link) Thank you :)
@MorganC-zz1bg
@MorganC-zz1bg 9 лет назад
I believe if you did some research into differentials and infinitesimals you would find your answer.
@harisrg92
@harisrg92 12 лет назад
Grade 11 mathematics.. Grade 12 mathematics.. and now finally University Calculus... and I know for sure in future azwell.. you are always going to be there to help me in Math..!! THANK YOU SO MUCH PATRICKJMT!!!!
@Darkray99EnMg
@Darkray99EnMg 10 лет назад
no entiendo ingles pero me gustan tus videos :)
@patrickjmt
@patrickjmt 10 лет назад
yo no hablo español , pero me alegro de que te gustan los videos!
@mage1413
@mage1413 12 лет назад
i said this in grade 9 once, and I'll say it again in my first year uni class....You are the best! most people would say that you're adding on to my teachers help, but I say that my teachers are just adding on to your help :)
@EngineeringNS
@EngineeringNS 9 лет назад
I love you.
@EngineeringNS
@EngineeringNS 9 лет назад
This was so confusing! But now I understand how simple it is!
@ak5504
@ak5504 11 лет назад
Dear PatrickJMT, I took Calculus I for Engineers at college without ever previously taking it in high school and I cannot thank you enough, because if it wasn't for you I wouldn't be one of the 3 people in my Calculus I class to have gotten an A, and beating the class average of 45%. Now I am in Calculus II for Engineers and I look forward to using your videos for this semester, and eventually next semester in Calculus III for Engineers! Thank You!
@sorianobellarmine18
@sorianobellarmine18 10 лет назад
How many papers have you gone through in your entire career of teaching math through videos?
@patrickjmt
@patrickjmt 10 лет назад
beats me. but considering this video has been viewed over 700,000 times, i would wager it is a pretty economical use of paper.
@sorianobellarmine18
@sorianobellarmine18 10 лет назад
It is. Thanks for all the videos. You rock.
@patrickjmt
@patrickjmt 10 лет назад
thanks nick, you are a stand-up kinda guy
@Getaneh188
@Getaneh188 10 лет назад
patrickJMT GREAT job! i don't understand my professor. I just use your videos. you must love maths.
@dirtbikedude91
@dirtbikedude91 13 лет назад
Good stuff. My teacher is a nice guy, but hardly even explained this... acting like it would just pop into out heads. Turned to RU-vid for help and found this video. It's so much clearer what we're trying to do now thanks to you
@quadhd1121
@quadhd1121 9 лет назад
I couldn't get how the 2x was delt with in the first example
@2013Aleksey2013
@2013Aleksey2013 8 лет назад
+Bley Mamwe He substituted du/2x for dx. ∫2x(u)¹⁰⁰du/2x = ∫(u)¹⁰⁰du
@FearDBro
@FearDBro 8 лет назад
+2013Aleksey2013 im still wondering why though. ok got it so basically he made a new equation that says its equal
@alekdanser
@alekdanser 8 лет назад
+Bley Mamwe that dt=2xdx
@Cholo95
@Cholo95 8 лет назад
I couldn't find a better teacher than you even at college, thank you so much for helping me to improve my grades in cal II 🌹🖖
@mrsilvxm
@mrsilvxm 10 лет назад
Have you ever thought about trying to get sponsored by Sharpie ??
@creampuff966
@creampuff966 6 лет назад
I'm pretty sure he is
@sophc193
@sophc193 9 лет назад
My calculus teacher made me hate math after a lifetime of loving it, and you reminded me what it's like to love it again. Thank you. :)
@kungaff
@kungaff 8 лет назад
Why do you "tack on" dx on right side when you are derivating both sides at 1:40? Confused :/
@RockOnDoooooooooood
@RockOnDoooooooooood 7 лет назад
You take the derivative of [u=x^2 +4] with respect to x. The real answer you get is du/dx = 2x • dx/dx. The dx/dx gets reduced to 1 and "disappears". Then we want to isolate du so dx is multiplied to both sides. These steps are inferred so that's why you just "tack" on dx on the other side
@sugarmagn0lia93
@sugarmagn0lia93 12 лет назад
I like that you explain using challenging problems. Not the prissy problems my professor uses that never show up on exams..
@Wewritestories
@Wewritestories 11 лет назад
why can't you teach my calc class??????
@xjoannaxx
@xjoannaxx 13 лет назад
Amazingggg! I'm not even in Calculus and I understand this more than Calculus students do because of you. Thank you so much!
@johncarloscorrea
@johncarloscorrea 8 лет назад
how do you get u to the 3/4 when you divide u by u to the 1/4?
@johnnyc4824
@johnnyc4824 8 лет назад
Dividing u by u to the 1/4 gives u to 3/4 because you subtract the powers when dividing. u by itself has power of 1. 1 -- 1/4 = 3/4.
@TheAwesomeNegro
@TheAwesomeNegro 13 лет назад
You're an absolute life saver! I'm attempting to switch from AB Calculus to BC Calc at the end of this semester, and these videos are really helping me catch up on some of the stuff I missed out on!
@noctisvaneixia4276
@noctisvaneixia4276 10 лет назад
what happens to the du?
@Syndicate6363
@Syndicate6363 8 лет назад
There's a reason your videos always have so many views, thanks man!
@kalef1234
@kalef1234 9 лет назад
omg get a pop filter haha
@hammyguybb25
@hammyguybb25 5 лет назад
puh puh puh
@lanceabagat2605
@lanceabagat2605 8 лет назад
Watched your videos right now bcos I need to pass calculus. Thanks, what a lifesaver you are. Two ups!
@gavin8988898
@gavin8988898 11 лет назад
Watching these video allows me to skip the lecture! The lecturer took 50mins talking about this and goes nowhere
@sheenazfazreennuryusof9980
@sheenazfazreennuryusof9980 10 лет назад
hey patrickJMT I just wanna give a huge thank you to you! your videos has been a huge help for me. in fact i understand better through watching your video than listening to what the lecturer teach! so thank you and continue doing an amazing job in helping others with calculus! :)
@aedanmcmahon1951
@aedanmcmahon1951 11 лет назад
exam today :(
@thewatcherlollol
@thewatcherlollol 5 лет назад
Howd you do
@frozenruby23
@frozenruby23 11 лет назад
I'm taking a first year calculus course and you honestly explained that so much better than my prof.... THANK YOU!
@alexanderedwards8863
@alexanderedwards8863 8 лет назад
hes left handed
@silverzero9524
@silverzero9524 7 лет назад
yup :(
@rozikhan2744
@rozikhan2744 6 лет назад
Nah camera is just flipped
@KillDevilXO
@KillDevilXO 5 лет назад
@@rozikhan2744 lol no it's not....
@YoshiPeach22
@YoshiPeach22 10 лет назад
If only I decided to get help through this way before I failed my first two tests and the midterm. Now I have to rely on my final to pass the class. It is tomorrow (or today actually). This helps make things crystal clear even better than the tutoring.
@aidanbelleau135
@aidanbelleau135 11 лет назад
bbuuuuuzzzzzzzzzzzz
@kevinl5972
@kevinl5972 11 лет назад
Patrick, you are my hero since high school! I'm a junior in college now.
@dop-a-meme
@dop-a-meme 9 лет назад
That irritating buzzz
@MultiGoban
@MultiGoban 9 лет назад
It calms me down, lol. I guess I'm lucky
@shin6997
@shin6997 8 лет назад
I'm studying engineering and your videos helps me a lot. More power!
@russiachan2
@russiachan2 7 лет назад
Now everything's starting to make sense. Thanks Patrick! You're a life saver!
@asinx6665
@asinx6665 7 лет назад
dude just know if i pass my exam on monday its all on you sir..great help
@MsToortle
@MsToortle 12 лет назад
Calc final tomorrow, teacher doesn't teach. You are my savior. Thank you SO much!
@ErinHopeful
@ErinHopeful 13 лет назад
You have made my night so much easier! I still don't understand the "why" of this substitution, but at least I know how to do it now! Thanks!
@SekaiiWorld2121
@SekaiiWorld2121 8 лет назад
I had no idea what was going on calculus, but I had a test the next day. Somehow, after watching your videos, I've been able to get a 106 on my test :') you're a magician!
@tahirsheikh8751
@tahirsheikh8751 5 лет назад
Literally have an exam in a few hours and u clearly explained a concept I missed. Thank you so much.
@KlasFerreira
@KlasFerreira 11 лет назад
wow, thank you man! I have tried to understand the substitution technique all week and I didn't understand it when our teacher talked about it. But now after 5 minutes it's easy as hell. THANK YOU!!! :)
@purpk86
@purpk86 11 лет назад
Ahhhhhh Patrick! I truly love your videos! Here I am taking second semester calculus and here you are helping me along the way. Thank you so much! You rock!
@scream4dreams
@scream4dreams 12 лет назад
i have a good math teacher, but i'd never be able to pass math 140 without you! thanks patrick
@tuomaskorhonen5260
@tuomaskorhonen5260 10 лет назад
Thank you thank you thank you! I spent 2 hours trying to figure out my math problems together with my teacher's answers and couldn't understand it at all. This really helped me!
@x3sianilia3x
@x3sianilia3x 13 лет назад
Thank you! I have uni exams in less than a week and I'm struggling with pretty much everything, your videos are helping very much. :)
@charlotteeduks4209
@charlotteeduks4209 9 лет назад
You're the best..don't wanna go for class..your videos are much better than class tutorials..its a headache to be in class..thanks..
@Nix-nb3zn
@Nix-nb3zn 3 года назад
exam tomorrow, and I swear when the prof tried explaining this exact same thing it was 10 times more confusing. god bless you dude
@etorres61
@etorres61 11 лет назад
Whenever I have a math question, I input the topic in youtube's search bar and I make sure to include patrickJMT next to it. Thanks for the help!
@RajShahlegandarystan
@RajShahlegandarystan 8 лет назад
Have my exam tomorrow, and you sir are my saviour. Very very helpful!
@rahil9386
@rahil9386 5 лет назад
You are really helpful my exam was there n I have not touched my book for whole semester so I was a lot worried but after watching your video my concept just got clear Thanks a lot
@hungryazhn
@hungryazhn 12 лет назад
hey Patrick! thanks for an absolutely fantastic series! i'm an electrical engineering student, and my calc is rusty for DiffEQs. these videos are clearing everything right up!
@lthatnemmyguyl1905
@lthatnemmyguyl1905 10 лет назад
Hey Patrick, recently started studying Engineering and your videos are great! I've gone from being a D- student to a A student in just a semester. Means a lot, and keep it up!!!
@HOneyyBrOwnx3
@HOneyyBrOwnx3 12 лет назад
cramming the night before my test tomorrow. you're a really huge help!
@patrickjmt
@patrickjmt 12 лет назад
my pleasure, glad i could help you for so long :)
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