Numerical Integration With Trapezoidal and Simpson's Rule

Calculus 2 Lecture 4.6: Numerical Integration With the Trapezoidal Rule and Simpson's Rule.

[@jeff9er615]

You should post a video of your workout routine, Professor Leonard. About the math, clear and concise. Thanks.

[@varunrajput3754]

yi

[@aintthatharsh]

@@varunrajput3754 yeet

[@yasirosman8242]

He is using the power rule for his workout lmao.

[@TheDagger55]

@@yasirosman8242 xD

[@Ko0okieeZ]

He uses math to get the exact number of calories needed for his diet

[@leonardo006]

Easy to understand. Not many professors connect with a beginner's mind like this, and just blabber on nonsense. Thank you Prof. Leonard!

[@Mikebigmike94]

Finally finished your calc 2 course, over 50 hours. thank you! I have noticed most university lectures it seems just more of a show of them showing how fast they can do maths, without teaching much, but you really take your time to teach and it shows. for example, your first calc 2 video was solely about natural log function and it was over 2 hours long. says it all :)

[@Eldricrypt]

says it all, just like your juicy pecs

[@jacobsteenhuysen7526]

You're currently educating Peace Corps volunteers in Indonesia. You and technology are amazing. Thank you.

[@ForzaAllegri]

Prof, I had the highest grade in Calculus 2, All my integrals were correct thx to ur great teaching! even In numerical Analysis I came back to u. You are the goat of teaching math

[@0zfer]

You are a GREAT professor. Can understand what you are saying, can read what you a writing on the board, you explain things very well, and you make sure everyone understands before moving ahead. Better then any real calc proff I have ever had. True story, last year in calc class I had this professor and I could not read his writing, we were in a room where the AC sounded like a jet engine and I could not hear what he was saying. I asked him, "could you please speak louder I can't hear what your saying". He said, "This room is louder then my typical room and I will not speak louder". I kid you not. I transferred out that day (thank god) and found he has a F on rate my professor. Later that semester some students went to the dean because they were upset and the school said they would do nothing. They gave all their names to the professor and he failed them all.

[@mikehensley7667]

I finished calc 2 in the spring and doing 3 in the fall. I felt I had some holes and wanted to find a way to review everything. These videos were a great fix. I picked up alot of new things I missed the first time around. This semester I will make sure to parallel topics with his calc 3 videos. Great teacher. Big fan. I watched every calc 1 and calc 2 video for summer review. I feel alot more confident going into 3 now.

[@utubefrog09]

My god, I go to CSU EB, I have taken Calc I and II multiple times and dropped them because my professors DO NOT explain anything, they just copy a set of problems from their notes on the board, I could get that using Wolfram Alpha. Thank you thank you thank you Professor Leonard, for once I could actually understand why we went from one step to the next, I wish we had a single professor 1/8th as good as you. Thaaaaaaaaaank U.

[@michaeldemontagne7366]

same here!

[@haydenmcdow7130]

The Knowledge Gainz are real. Thank you for the awesome video, made the Simpson's Rule concept much more clear to me!

[@myuse7848]

7 years later! Can understand it crystal clear! 30/08/2021 All the way from Sri Lanka! Thank you Professor!

[@gracenyambura9287]

I know this is like 4 years later but just thought you should know that you are such a life saver you have no idea

[@derickpambah]

Man! I am humbled by this guy. You deserve alot more here. Thanks once again. I hope you're fine where you're. May God bless you man.

[@johnmwajinje1941]

Watching the video from Kenya,,,thank you sir for helping me understand Simpson and Trapezium rule

[@cr7neymar908]

Just finished my calc 2 class with a score of an 101!!! Crazy to think that just a year and a half ago I was in the army taking elementary level math classes at my college. Off to calc 3 to finish this off

[@swimtothetop]

Just took my calculus 2 final, aced it! Thank you for all your help Professor Leonard, because of you I'm done with calculus 2, now on to calculus 3! :D

[@chris-dd6uq]

@Maher Arora How was Calculus 3? How was it compared to Calculus 2?

[@swimtothetop]

SKYNET #2025 I thought calculus 3 was alright. probably easier than calculus 2 but 3 is very abstract. there's a lot of abstract concepts and it is helpful if you are able to grasp these different multi dimensional concepts.

[@chris-dd6uq]

@Maher Arora Thanks. Have you also taken Linear Algebra? In my school Calc 3 is a prerequisite for Linear Algebra. But I want to take them at the same time. I'd have to get permission first. Do you think that it would be a bad idea to do so?

[@swimtothetop]

SKYNET #2025 linear algebra and calc 3 go hand in hand. I took Lin alg first and it was easier than calc 3

[@chris-dd6uq]

Maher Arora thank you for replying to my comments.

[@LuYi404]

SPEECHLESS!!!! AMAZING. The best Pro-Professor in the world! 🙏👌

[@JoseOrtiz-dl5wc]

Literally was your student for the whole a semester, now time to drive it home by practicing examples, so that I may pass my calc final.

[@bLittleHemi]

You have to come to New Mexico State University and teach Calculus 2!! My professor couldn't make numerical integration this simple and easy in a hundred years! You are awesome, brother. Keep it up!

[@seendidthegreat4814]

I took this course over the summer so its a six week course. Its mainly for people retaking the class. Most of the first timers are overwhelmed. I had professor leonard and ive never felt more confindent before. It feels so amazing to finish your calc2 series. After my exams it will be on to calc 3!

[@georgesadler7830]

Professor Leonard, thank you for an awesome video/lecture on Numerical Integration with Trapezoidal and Simpson's Rule in Calculus. These are two classical Techniques of Integration provided that the limits of integration are provided. I watched, analyzed and take notes on all 27 videos in the playlist and the explanations are off the learning charts. Professor Leonnard, you are one of the great teachers in the classroom and on KZbin. There are few errors in this playlist and they are corrected by the great viewers.

[@vtecminileon]

Thank you very much. Absolute legend!! Your teaching is clean and crisp. Wish we had a teacher like you.

[@mimicmemento]

You are a lifesaver! My professor explains things in the weirdest ways possible, and uses "shortcuts" that don't always work and aren't actually mathematical (so coincidence). Your lectures help me with the topics that I cant understand my professor for! I definitely wouldn't be able to pass this class without these lectures, thank you so much!

[@mortiloniperpomontinson]

Log

[@dpmike32819]

You’re still the man… Still enjoying your videos… even at 72 years old

[@Iz_moe]

My professor overcomplicated this way to much. This is easy, thanks Prof. Leonard

[@keroloskaras7973]

I had no hope of passing this class, and I started watching your videos after half of the course finished. Guess what I passed. I really can't thank you enough!!

[@henriqueoliveira3872]

Jesus, you also do Computational Mathematics. You are an absolute legend sir. Thank you very much.

[@firohd8748]

Prof,you are genius u give the lecture easily and smartly keep going sir I appreciate that

[@SeriZawa7743]

I have got a numerical methods paper tomorrow ... you just saved my life ... Thanks a lot

[@birincitekilsahs963]

someone chews gum during class and it is very annoying but this video is very beneficial, thank you professor :)

[@laforever401]

I'd kill to have you as my math professor. In academic language, if you were teaching at my unversity, and spots weren't available (for obvious reasons), I'd literally wait until the last semester before my graduation just to take you for calc 2. That being said, I don't know how to thank you enough. You've helped me A TON with these videos! God bless you!

[@modesteakouete2473]

i wouldve failed my class without your videos thanks Professor Leonard

[@asiimwemicheal53]

u have saved me tomorrow i have a paper of numerical method thnks alot

[@isaacroush2674]

This video helped so much!!! I had no idea what I was doing before, but now I totally understand. Why can't all teachers be like this????

[@beoptimistic5853]

kzbin.info/www/bejne/nIPchpljfL5qa5Y.

[@MisterFusion113]

This teacher is off the charts.

[@RedStormLax]

You explained this far better than my college professor did in 27 minutes and he's had two lectures.

[@virginiabushnell3042]

I watched your calc 1 lesson 1 video this summer while tripping hard on shrooms and lsd and it motivated me to transfer my credits and take calc 2 even though I did terrible in calc 1 yrs ago., like 70% terrible. Totally understand everything in calc 2 so far though and very excited about it! Gonna watch this video later. Anyway thanks!

[@xxsaifxx2450]

bro without you i would fail engineering what a true legend

[@petermiller5659]

im from the philippines. im not around when my prof taught this coz im working. now i could go face exam tom. ty so much!!!

[@Nonynonza]

Easy and fast. This just saved me tomorrows final! With all due respect to the masses of hindi videos out there, I think a lot of us needed this :b

[@mashfique1]

thanx proessor..i have been watching your videos to get my concepts clear and every time i miss class....have to say...one of the few times internet isbeing used to gain positive learning experience and notkilling time....

[@forexdailyearnings]

I am from pakistan, and i love your lectures, easy to understand... thanxx

[@fatemehasgarinejad]

You have no idea how great you explain things. Thanks!

[@beoptimistic5853]

kzbin.info/www/bejne/nIPchpljfL5qa5Y .

[@user-cl6yd2wk5j]

Anybody else raising their hand and answering his questions like you're in the class and not watching it six years after it was filmed?

[@ezeemmanuel7591]

You are naturally born tutor. Subscribing already.👍🏻

[@EugeneWasSeen]

Great video. One thing I'd suggest is sketching a graph of the trapezoidal rule to visually see where the formula comes from.

[@greense65]

I'm with Prof. Leonard on this one. I suggest going to the book for anything more on approximation of integrals. These techniques used to be important, but now they are much less so. Prof. Leonard just gives them a quick nod. These approximation techniques are now most easily accomplished using a spreadsheet. But if you have a computer to do that, you have access to extremely accurate integration software, and so don't need these approximation techniques.

[@fatih.cevahir]

Hello From Turkey. I dont speak english but I understand you. Great Teacher Thank you.😊

[@dmanola7able]

Thank you for relating this material in a clear manner! you explained it way better than my professor

[@-AnweshaDas-]

you're a great teacher! Thank you so much for this. It was very helpful. 💙

[@yazmingonzalez7965]

I love this teacher. This is going to help me on my Junior Calc II test tomorrow

[@wealthoceans7348]

your the best sir!!!! This year I am going to get graduated and you were the one who helped me to cope with my applied mathematics 3 course!! Leo, THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@FarisAlmaymani]

Thank you very much. I didn't understand from my doctor face to face, But I really understand all things about this from you My exam tomorrow and I really need this. Thank you very much

[@brightfutureacademy2323]

بہت اچھے سر مجے آپ کی ویڈیو بہت پسند آئی ھے

[@muneebow]

I swear to god this guy is the Superman of math :D

[@victorserras]

Just explained perfectly and in less than 30 minutes what my teacher failed to explain in 2 hours.

[@matthewconsidine2492]

Let’s make this guy a millionaire 🎉

[@Ridgerunner2270]

This was very helpful for my Numerical Methods class. Thank you Professor Leonard!

[@kirubelayele5734]

you were amazing.Please keep teaching students need you much more. Thank you.

[@ifahad4067]

the best math teacher ever .. thank you

[@andreaskoutsogiannis5795]

I love you PROFESSOR Leonard you're the MAN the MYTH and the LEGEND!

[@rosukiii.]

This is awesome! Last thing I needed to know for my recovery exam. Challenges made easy

[@drinkgreen]

Great video. This helped with studying for my Numerical Methods final

[@adeolajoy4539]

It was understanding to some point before I got lost and have not been able to find myself but it's a well done work sir 😊

[@codewithmarwan]

You are a savior, Best teaching video on youtube I have ever seen, keep up the good work, Subscribed already

[@siamtowhid3505]

You Sir is a real life super hero. Thank you so much!

[@angel19955991]

Finishing calc 3 was sad knowing that i wouldn't have your help for differential equations professor... however, it's nice to have your videos as a review 100% every time

[@siyabulelamanona1438]

Thank you so much Prof. Very clear and easy to understand. You’re a superhero Sir.

[@vayneshade]

You are the saving grace that compensates for my shitty numerical methods professor, thank you so much!

[@Heldawm]

It was very clear. Thank you, from Brazil.

[@fredanisi2364]

Really awesome. Everything was really easy and seems to be pretty understandable. Thanks very much sir........

[@ducky2676]

Nice and clear discussion! .thank you for uploading this kind of videos it's really helpful.

[@alexandercervantes1078]

Awesome video! I missed the lecture in class, but this was an excellent alternative and I fully understand this section! Thank you.

[@AnthonyGosal1452]

I had a great time watching your lectures;thank you so much for posting these. I look forward to your calculus 3 series and will be sure to watch calc 2 again when the nostalgia hits!

[@TheFunkyCriminal]

great lecture, definitely gonna keep watching

[@jyamijuice9100]

best math teacher

[@martialway100]

Thanks for the lesson. Everything was well explained, apart from the final change of substitution integral in the Simpson's method. The limits should have been from 1 to 3, as the sub. was U=X+1 not 0 to 2, in the newly formed 'u.du' integral. The answer was right, as you converted back into the x independent variable and substituted the original x=0 and x-2 limits. Not a big deal, but at A Level and degree level, you'd lose a mark or two for the incorrect limits in the 'u.du' integral. Apologies for being overly pedantic on this one. :-)

[@toast072]

Just a suggestion, that was very clear, but I think it would be easier to see if you also include a graph to show visually what is happening.

[@greense65]

I'm with Prof. Leonard on this one. I suggest going to the book for anything more on approximation of integrals. These techniques used to be important, but now they are much less so. Prof. Leonard just gives them a quick nod. These approximation techniques are now most easily accomplished using a spreadsheet. But if you have a computer to do that, you have access to extremely accurate integration software, and so don't need these approximation techniques.

[@karikaranvetti4897]

i enjoy your lecture sir thanks a lot from SriLanka

[@darimuhittin]

Beautiful explanation. Thank you sir.

[@hassanalabdullah8814]

calculus 2 lectures done, thanks prof

[@sameerrajput8732]

गुरु जी धन्यवाद आपका आपने काफी अच्छे से हमारी शंका का समाधान किया

[@sangyaltsering7645]

Awesome video!!! plz, keep your work continue!!!

[@henri1_96]

PC principal is doing God's work by uploading these :)

[@jeffreygomez7360]

Thank you, u basically summed up n entire chapter section I couldn’t understand, nice vid

[@cinnamonspicelatte3124]

Everything's fantastic! The only error I noticed is that when you do the u-substitution for the last integral (around 26:00), the bounds change when you write it in terms of u to 1 and 3, and the dx should 'change' to du, since we're taking the integral in terms of the variable u. Other than that, great video!

[@Mathematicsketeacher]

Very helpful and informative

[@girawatube2334]

i loveeeee uuuuuuuu professor leonardo am gonna to be a lecture of calculus by the case of u.thankkkkkkkkkkssssssss alot.from ethiopia

[@sadrazargarbashi3952]

جوون چه خوبی شما پروفسور

[@faheemahmad5882]

why on earth u have 468K ? u deserve millions

[@beoptimistic5853]

kzbin.info/www/bejne/nIPchpljfL5qa5Y.

[@hussamcheema]

kindly make a series of Linear Algebra too.

[@milesdavidsmith]

Very good teacher!

[@fafiethamae]

❤thank you , you've just saved a soul from failing hahaha ... Am gonna come back with my results 🙂🙂🙂

[@msjahun]

prof. you're a life saver.

[@iqmahoseni4268]

Thank you 😭 I'm from Nigeria and this helped thank you so much

[@davidedmundtochi5228]

Nigerian👊✊

[@beoptimistic5853]

kzbin.info/www/bejne/nIPchpljfL5qa5Y.

[@henrygarcia1152]

Prof Leonard is the man

[@MarkoVrbos]

At 25:17 should be "du", not "dx"... :-D Awesome teacher, I'm watching these videos even though I got my master's 15 years ago :-D

[@jmathsjmt]

Nice explanation sir

[@donyagoodarzipour5720]

You sir, just saved my life, god bless you stranger XD

[@beoptimistic5853]

kzbin.info/www/bejne/nIPchpljfL5qa5Y.

[@fatimacacho3758]

If you're looking for a video that will help you understand how the Trapezoidal Rule was derived, this is NOT the video for you. He reminded you the basics of integration and then showed you how to plug things into an equation. I didn't even want to watch his explanation of Simpson's Rule (which is why I came here in the first place, Khan Academy didn't have a video on Simpson's Rule) because he started by just erasing numbers and replacing them with new ones without an explanation. If you want a more in depth explanation of either rule, this is not the video for you.

[@mxkep]

Very helpful on my course in Numerical Methods. Thanks!

[@FancySparrowGames]

Thank you this helped me to do a home work !