We certainly live in a golden age of knowledge when you are able to study with marvelous teachers like these from your own home. Superb and elegantly explained.
@LastMinuteGuess
5 жыл бұрын
@DYNAsty Maybe they just choose to diversify their personal time in other activities they find more productive and fulfilling.
@hilariousharry1890
5 жыл бұрын
@@LastMinuteGuess that's correct dude
@dianampm99
5 жыл бұрын
@Thug_Jitsu then your university is not giving you enough work if you have 8 hours to spare every day...
@rijulranjan8514
4 жыл бұрын
D Padilla I mean I doubt it with a school like Umich. One of the most rigorous engineering schools in the nation
@ejay1836
2 ай бұрын
high quality education
@darthboganis1356
4 жыл бұрын
Trig integrals: sin^n(x)cos^n(x) 0:00 Case 1 odd powers 3:00 Case 2 even powers 7:30 Example 1 odd powers 10:00 Example 2 odd powers 18:30 > one is odd: strip off one factor, apply Pythagorean identity, then use substitution [22:20-24:00] > both are odd... pick the smallest power Example 3 even powers 27:30 - use half-angle formulas > make all sine or all cosine, e.g. double angle identity [29:35] > reduction formula revisited 32:15 (the sine power is greater than 2) > half-angle identity 35:00 > problem continued, what now? 40:00 > quick review of process 42:00 >The half-angle identities reduce the power. We want to reduce the powers to 1, which makes integration easier Trig integrals: sin^6(x) 49:00 no reduction formula: use even powers >> half-angle identity distribute using binomial expansion Continue removing powers 53:30 i.e. half-angle/pythagorean application Trig integrals: sin^n(x)cos^n(x) 1:10:11 > similar steps taken as per above Trig integrals: tan^n(x)sex^n(x) or cot^n(x)csc^n(x) 1:24:00 > the idea 1:34:30-1:36:30 > examples 1:36:30 Trig integrals: cot^n(x)csc^n(x) 1:51:00 Reminder on principle 1:53:30 When they don't fit a readily solvable pattern 2:00:00 > rewrite in sin and cos terms to fit the pattern. consider identities Different angles for sine and cosine 2:08:00 > using identities to solve these problems 2:10:30 > examples 2:13:00
@ethanwilks5510
4 жыл бұрын
Thank you for this
@aneeshussain6200
4 жыл бұрын
Good job
@mhararizmarino8897
3 жыл бұрын
Thank you so much! :)
@rawadhasan9111
3 жыл бұрын
thank you! this should be pinned
@paulschuebel5487
3 жыл бұрын
Stripper joke 11:00
@onyxa3144
3 жыл бұрын
This channel is single handedly going to save my grade in Calculus II
@SNoCappidona
6 жыл бұрын
"people take calculus II to finally fail trigonometry" exactly how i feel lol.
@39dkwj
4 жыл бұрын
too true :/
@Peter_1986
4 жыл бұрын
I prefer to think of it as "people take Calculus II to finally NAIL trigonometry".
@amandasd9061
3 жыл бұрын
Bruhhh.. I’m taking calc 2 and like oh you really wanted me to memorize the trig circle
@templeknight9338
3 жыл бұрын
yeah that really discouraged me
@Squash101
Жыл бұрын
@@templeknight9338 just learn trig from him took me around 2 1/2 days to essentially learn all of the important trig shit
@mf9389
10 жыл бұрын
i think its rlly cool that when you press that button on my face you change shirts and clean the board so fast
@essayprometheus
3 жыл бұрын
LOL
@joshuagaa7009
3 жыл бұрын
that's superman for you. Lol
@nickfruneaux5232
2 жыл бұрын
these videos are consistently so good because Prof Leonard takes the time to actually explain the logic behind things, in an efficient but necessary way, whereas so many math textbooks / explanations take critical assumptions for granted and jump to conclusions in a way that a student might not easily follow. really great!
@Erik-pu4mj
4 жыл бұрын
Quality content still getting word-of-mouth recommendations years later. Thanks, Prof. Leonard!
@EagleLogic
7 жыл бұрын
I can't imagine how incredible it would be having a professor like this... Right now I feel like I am taking cal 2 twice since before lectures I watch the material we are going to learn in my class on your channel and then I go to class.
@lwazipress5224
9 жыл бұрын
Proff Leonard I think you was born to teach calculus,you remove a lot of confusion to me and I pass calculas 1 because of you and I'll also pass calculus 2,what are you doing is very helpful to many students, so I just want to say THANK YOU VERY MUCH Proff MAY GOD BLESS YOU!!!
@ElizabethRey97
8 жыл бұрын
He already blessed though. That brain
@danialdunson
5 жыл бұрын
@@ElizabethRey97 that reply
@saint_1837
10 жыл бұрын
Professor Leonard, you are an actual teacher. And America (the world) needs more people like you. I appreciate your work and your skills. Keep it up. Thumbs up.
@skywolf6984
9 жыл бұрын
America ( the world ) he says , laugh with my ass I said . lol
@lionesscan
9 жыл бұрын
Sky Wolf HHAHAH
@lionesscan
9 жыл бұрын
Sky Wolf ME TOO:D
@skywolf6984
9 жыл бұрын
Nah ofcourse I dont , but you might be thinking with your ass due to your answer.
@hotghettoliquid
9 жыл бұрын
What impresses me about this guy is the laser precision of his lectures. He obviously processes this stuff at light speed, but he seems to slow the reference frame down for everyone else because of his smooth and methodical approach. This makes the Calculus far easier to digest. Having command of a 2+ hour video like this is no easy task. Thank you Professor Leonard!
@MeistroJB
8 жыл бұрын
You know I,m engaged with the trig integrals when I start raising my hand when Prof. Superman says, "Show of hands...." - from HERE (B-more, MD)... Thanks Prof. You 'da best.
@Wehere968
5 жыл бұрын
I swear to God you are the G.O.A.T. I have never seen a maths professor this good and simple. You made me get an A in calculus 1 now let's see about calculus 2.I gonna start calling you my secret weapon. Thanks a lot.
@Robot_Chimp
7 ай бұрын
What grad you get
@plus_osu
3 ай бұрын
@@Robot_ChimpE
@manueldouglas5180
2 жыл бұрын
Spent the whole day watching the video and going through these examples that I felt that I was a part of your class.. Thnnk you for making maths interesting and fun
@sheepman6291
7 жыл бұрын
With your classes I'm pretty much am going to finish 2 calculus classes in one semester, and you're going to save me 700 dollars.
@viviandingdong
6 жыл бұрын
I literally left my lecture hall to come watch you explain it because I understand you way better. God bless you, Professor Leonard
@joebrinson5040
3 жыл бұрын
As a retired high school math teacher I love to watch you teach. You are the best!
@italianmofo4037
7 жыл бұрын
I kinda feel empty inside when he finishes a 2 hour lecture and i have to return to reality and to the fact that I'm bad at math.
@nitotech
6 жыл бұрын
How does one do better at math? They do them on their own.
@jacobl.743
6 жыл бұрын
You're not bad at math. It's just a ton of practice
@Carnezz
5 жыл бұрын
The only way you can be bad at something is if you don't do it enough. Just practice and you'll get it with time.
@GoatzAreEpic
2 жыл бұрын
I failed my calc 2 class and am now watching your videos and it's so clear to me now
@ZephKin
9 жыл бұрын
Hooray, a good professor I can understand without an accent/2nd language getting in the way... Seriously. You are very clear. Thank you. I don't know if I can make it on my own sometimes going to some Calculus lectures. You have your act together focussed on teaching students. Quality. Props. You must care for teaching others. The world needs that integrity for it to continue functioning.
@akeembobo8530
8 жыл бұрын
I will find you and you will teach me.
@cottoncandyflossful
8 жыл бұрын
I like how you explain things so clearly.. I am doing A levels and my math teacher is.. well.. too good in math and that makes him bad in teaching. He does integration at lightning speed and it is just so hard to understand his short and overly simplified workings. I am so glad i found your channel!
@TheHotOnes0
7 жыл бұрын
Professor Leonard you're one of the best professors in the United States! My calculus 2 teacher isn't anything compared to you.
@SharjeelTahir-lq3tx
Жыл бұрын
Great videos. Reviewing calculus after 14 years to do machine learning. I wish I had these videos available when I was in freshman year.
@koomoo
7 жыл бұрын
Hello Professor Leonard, Thank you so much for making these videos. It has helped me a lot in parts i did not understand while in class. The step by step instructions and going back to explain how you got some answers makes things so much more clearer. Everybody have different ways of learning. Your style is best for me. Thank you.
@silentthriller
7 жыл бұрын
I'm pretty sure someone said this already, but sin(x/2)(half-angle) != sin^2(x)(Power-reducing). Just a clarification. Professor Leonard's videos help a great deal. Carry on.
@musaarab5581
7 жыл бұрын
Thank you professor Leonard, my teacher sucks at explaining the simplest of materials. You make the hard things simple (:
@erickrobles6365
8 жыл бұрын
I considered myself a master at integrating last summer when I was taking Calculus 2. Now i am taking linear algebra and differential math this semester, and man, prof. Leonard is a integrating hero. Btw. your new movie coming out! Batman v Superman!
@erickrobles6365
7 жыл бұрын
linear algebra no. I meant vector calculus, sorry
@ItsRawrTopia
7 жыл бұрын
What was the hardest for you? Calc 2? Calc 3? Linear Alg + Differential Equations?
@hadis9109
5 жыл бұрын
Calc 2 is usually the hardest@@ItsRawrTopia
@andresdelgado5892
8 жыл бұрын
Thank you for these videos. I spent days working on 8 problems from this section and was completely lost. I finished my homework minutes after watching this video. I will definitely continue watching!
@AliYoussef-oo4oe
Жыл бұрын
man, i truly appreciate what you're doing. i love you
@mitchs8011
9 жыл бұрын
very helpful. you are like the Chris Traeger of calculus.
@excellentngidi
3 жыл бұрын
Thank you Proff even though I'm always raising my hand when i understand like the rest of the class😀😀😀
@gatw1977
3 жыл бұрын
An interesting thing is that Prof's classes are super interesting, not boring. I mean,look at me staying for a "more than 1 hour" video
@crawdkenny
4 жыл бұрын
I love the ads on these videos where they talk about how all the math videos on KZitem are old and unhelpful. These videos of course come before the best and most helpful math teacher I've ever seen.
@kamrankerim636
8 жыл бұрын
You are blessing from God for my calculus course! thanks a lot, Professor Leonard!
@SeasonedTofu
5 жыл бұрын
Thank you for posting these lectures. My Calc 2 professor does not explain anything like you do. He doesn't even give definitions, he just throws a problem on the board and solves it in front of us and expects us to just get it. My first test is in 4 days and I've been watching your lectures. It god bad enough to where nothing he said even made sense that I just gave up and opened up my laptop, threw in my earphones just to watch your lectures during my actual class. Thanks for always reminding us of trig that we should have remembered but forgot. You're a god among men, also great gains bro.
@georgesadler7830
Жыл бұрын
Professor Leonard, thank you for an exceptional video/lecture on the Techniques for Trigonometric Integrals in Calculus Two. Many Trigonometric Integrals can be solved by using Sines and Cosines/converting Trigonometric functions into Sines and Cosines. A solid background in Trigonometry is needed for Trigonometric Integration.
@xzavierreed
Жыл бұрын
I’m taking calc II this summer, and man have you been a god in the maintenance of my A in the class but actually applying it [casually] in other subjects pertaining to my degree.
@akelmaseka9385
6 жыл бұрын
You are the best Math teacher ever. May God bless you with more success and happiness for uploading these awesome videos on KZitem and making them accessible to all engineering students in the world.
@anas8296
Жыл бұрын
professor Leonard has caps lock on
@tresory3944
3 жыл бұрын
Thank you professor for everything you do. My friends and me are following you from France. God bless you!!!
@Saab469
2 жыл бұрын
definition of a blessing thanks so much
@santiagobenitezperez5240
2 жыл бұрын
Professor Leonard has helped me study calculus. Thank you very much!
@scottdixon9415
9 жыл бұрын
Professor Leonard, thank you for posting these. I'm preparing for a Calc II final, and your videos are excellent review.
@moshwanalebogang9528
4 жыл бұрын
how do we repay you or give thanks... you are truly the greatest, because of you i hardly even attend my math lectures anymore... keep it up
@muh.hamiddd
27 күн бұрын
Thank you so much Professor Leonard, You're my Calculus hero.
@stephanieweil178
3 жыл бұрын
"There's something a lot of you love to miss, what is it?" Me, simply a common viewer: PARENTHASES!!!!!
@krystiantomczuk7451
7 жыл бұрын
Awesome teacher! I use your videos to supplement my Calc II summer course, they are helping a lot! Thanks!
@Maheed94
9 жыл бұрын
This is AMAZING!! Thank you so much, Professor Leonard! This helped me a LOT, I can't even explain! Much appreciated.
@Mikebigmike94
2 жыл бұрын
legend. every video I watch I leave with a hell of a lot more knowledge. might be worth watching this lecture twice to nail it home!
@jasonyang6738
9 жыл бұрын
thank you so much for giving not only me but also those people who are watching this video an opportunity to study Calculus. I have to say you teach so well, I just need watch it once and then totally understand it.
@user-du4cy9ff5p
8 жыл бұрын
it really helped l was sick and not able to went to lectures. tomorrow is my mid term test your video really saved me thank you so much
@fuckit5447
Жыл бұрын
I've been so lost on trig intergals this video is literally a gold mine that's gonna save my final grade
@KLCII88
8 жыл бұрын
I wasn't able to make it to class tonight but thanks to Prof Leonard I didn't miss the lecture. Thank you sir!
@teutah966
3 жыл бұрын
I have a calc 2 midterm on Thursday and this prof helps me 10000000x more than my own prof who told us to "teach ourselves" every chapter and shows very few unfinished examples
@emmanuelakindele5051
Жыл бұрын
Not me raising my hand lol. 😅😂
@FlooRazkalz916
10 жыл бұрын
I appreciate you posting these videos, these help me prepare and review for my coursework. so thank you... also you crack me up when you say "Yay!"....LOL
@kingcvm1
8 жыл бұрын
Professor Leornard- I have a test this week and I love your videos like everyone else. Do you have any videos for arc length and area of a surface of revolution? They are sections 8.1 and 8.2 in my Calculus book. Thanks for your response!
@ProfessorLeonard
8 жыл бұрын
+xfa xdfa Should be found in my calc 1 videos. Lecture 5.3 or 4 if i remember. Good luck!
@kingcvm1
8 жыл бұрын
Thank you. I spent the weekend watching your videos and everything is clicking. Appreciate what you do
@selmanabd2782
8 жыл бұрын
+Professor Leonard thank you sir you are the best teacher that i have ever seen
@jorymalallah4463
3 жыл бұрын
my friend reem and I love the way you teach your students, they won’t be bored from watching your explanation because of your amazing way in teaching. your fans jory and reem from Kuwait , god bless you
@kqnrqdtqqtttel1778
3 жыл бұрын
Self studying Calc in middle school is quite fun :)
@user-si6ey2gq4t
Жыл бұрын
Professor leonard taught me more than my teacher 🤣, my teacher just gave the formula but not explain where it spring from
@chelseareed2373
9 жыл бұрын
I wish I had you as a teacher. you're awesome , 5 star !
@mdotani
8 жыл бұрын
You are awesome! Thanks for putting these videos up. Saved my life for calculus II!
@rawan95B
9 жыл бұрын
Thanks for being so awesome ! Now I have more confidence in my math skills and I'm ready to ace my test tomorrow .
@sandisombanjwa2813
5 жыл бұрын
THE REAL SUPER MAN IS PROFESSOR LEONARD He can change his clothe without anyone recognising. like Super man when he is about to save someone from trouble.👍👍👍👌🙌 thanks prof
@TK3C
9 жыл бұрын
Shredded as fuark.
@alaadeiri7789
8 жыл бұрын
thank you very much professor leonard i finally understand calculus
@danialdunson
5 жыл бұрын
you are the most down to earth math professor. thank you for your simple explanation and tips! so much help.
@johnkisserliss4280
2 жыл бұрын
Professor Leonard in one of your examples towards the end of the lecture you put 328/231 I am getting 131/231. ( 77+33+21)=131 I hope you can explain to me how you got 328 all the best John
@Aman3c3r
9 жыл бұрын
thank you Professor. Your videos had helped me a lot during my Cal II class!
@nehemiahshiwayu9224
Жыл бұрын
Thank you very much sir for the helpful video !
@Roman.Yuhaev
5 жыл бұрын
Certainly a pleasant lecturer, it's fun to watch even though you know the material. Best regards from Israel!
@janenguyen8924
9 жыл бұрын
you are the best math teacher ever. I love calculus and hate regular 8th grade math.
@Enlightenchannel
2 жыл бұрын
I love when he imitates an angry student "Where are they getting 1/16th from!" It's embarrassing because I know that's probably exactly how I sound. Just shouting "WHAT IN THE ACTUAL FUUU.... Oh... Oh yea I have to square 1/2"
@mariec.4516
8 жыл бұрын
If you were my teacher in integral calculus i'll always attend your class and listen for real 😂
@Love001u
8 жыл бұрын
+Marie Cantos hahaha meee too! 😂
@ruskodudesko9679
8 жыл бұрын
you should do that to any class lol wtf
@arulgk9673
5 жыл бұрын
rusko dudesko Its not that we don't want to, it's boring af
@jorymalallah4463
3 жыл бұрын
hello professor , the way you teach your students is amazing, can’t get bored watching your explanation, god bless you professor, your student ( Kuwait )
@jorymalallah4463
3 жыл бұрын
your students jory and reem from ( Kuwait )
@Justin-jj4zq
6 жыл бұрын
Its painfully clear that trig is what is holding me back... Just took my first calc 2 exam and completely failed, mostly due to trig stuff! So frustrating, and I am less than a semester away from my Associates Degree so its too late to go back now... :( I am just hoping that watching more of your videos will help me out, Professor Leonard. Thanks for doing this, its nice to have a teacher to refer to when I am at home as well.
@lovecake9879
3 жыл бұрын
thank you brofessor biceps
@awakinteh8599
3 жыл бұрын
You are the best, really love the way you teach. I will love to see your test papers and homework. So i can challenge myself
@Alsharef360
7 жыл бұрын
Bodybuilder and math teacher
@whitb62
5 ай бұрын
We didn't learn the flipping the integral/changing the sign thing in Calculus I. That's very cool.
@MoazMohamedEldamery
5 ай бұрын
u r the goat
@TheBigMeme67
2 жыл бұрын
God bless your soul Leonard. Just finished C1 onto C2
@coreydevs
2 жыл бұрын
Thank you for wiping the board clean every time. My professor leaves so many marks when erasing and I spend half the class thinking about it.
@syrenka6
5 жыл бұрын
Thank you for all those videos
@bladehowell
9 жыл бұрын
PLEASE DO CALC 3 & 4. this is great.
@ItsRawrTopia
7 жыл бұрын
You mean linear alg + Differential Equations IKR we need that
@restitutororbis964
6 жыл бұрын
Wesley Howell there isnt isnt a calc 4 lol, there is tensor calculus tho if u meant by calc 4. Then after that comes linear algebra then differential equations, then linear differential equations
@yoyonostring2147
5 жыл бұрын
Calc 5 too
@Atractors
4 жыл бұрын
This is very nice explain integration some trigonometry functions. Thank you for material.
@hindj9142
2 жыл бұрын
Thank you so much professor. You’re the best
@nishadr.7637
3 жыл бұрын
Watching lecture videos like this one make me realize just how much I miss in-person classes.
@HY-bo9nt
10 жыл бұрын
Thank you so much for sharing this video !
@rumpelforeskin8461
7 жыл бұрын
I have a garbage calc 2 teacher! Thank you Professor Leonard for all of your help.
@gauravmodak3491
4 жыл бұрын
2019.... the legend continues.... long live math
@Love001u
8 жыл бұрын
sorry for my new teacher that i have for cal 2 but you sir Leonard, you have made section 7.2 very clear for me ^_^
@Maliceking
6 ай бұрын
This guy is such a chad
@ephysi
7 жыл бұрын
from morocco you are the best!!!!!!!!!!!!!!!!!!!!!!
@Cirius-wl2xr
2 жыл бұрын
With even powers come from even responsibilities.
@robertcoggin8300
8 жыл бұрын
6 people who hit the thumbs down button on this video.. 6 people who somehow didn't find this helpful who PROBABLY need to change their majors to something less "mathy" if they still don't understand calculus even after watching Professor Leonard... lol
@kittycat1768
8 жыл бұрын
To be fair, some people were not equipped with a sufficient background to advance into calculus during high school. I, personally, have just finished my first year of high school, yet had to teach myself a college trigonometry course before I could understand a fair chunk of calculus- prealgebra, algebra I & II, geometry and trigonometry are simply brushed over in a sequence of three general math courses at my school (Math 10, 20, optional 30- you graduate). Those who don't understand such simplified explanations need to supplement themselves with more algebra and trigonometry, not switch to a philosophy major.
@cliffordkasulimwachunga6215
5 жыл бұрын
He is my best prof.
@samzheng9899
7 жыл бұрын
Prof.Leonard is much better than most of "professors" in my college
@LandonOhanian
2 жыл бұрын
11:52 the board 12:13 two odds with multiple XS 1:12:13 integration with limits
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