Numerical Integration With Trapezoidal and Simpson's Rule

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  • Опубликовано: 24 дек 2024

Комментарии • 309

  • @leonardo006
    @leonardo006 8 лет назад +90

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

  • @Mikebigmike94
    @Mikebigmike94 2 года назад +34

    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
      @Eldricrypt 11 месяцев назад +1

      says it all, just like your juicy pecs

  • @jacobsteenhuysen7526
    @jacobsteenhuysen7526 8 лет назад +83

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

  • @0zfer
    @0zfer 9 лет назад +9

    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.

  • @ForzaAllegri
    @ForzaAllegri 4 года назад +14

    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

  • @jeff9er615
    @jeff9er615 10 лет назад +540

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

  • @mikehensley7667
    @mikehensley7667 4 года назад +9

    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.

  • @haydenmcdow7130
    @haydenmcdow7130 8 лет назад +45

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

  • @utubefrog09
    @utubefrog09 8 лет назад +49

    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.

  • @gracenyambura9287
    @gracenyambura9287 6 лет назад +3

    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

  • @myuse7848
    @myuse7848 3 года назад +4

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

  • @derickpambah
    @derickpambah 3 года назад +5

    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.

  • @maher_arora
    @maher_arora 9 лет назад +65

    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
      @chris-dd6uq 7 лет назад

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

    • @maher_arora
      @maher_arora 7 лет назад

      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
      @chris-dd6uq 7 лет назад

      @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?

    • @maher_arora
      @maher_arora 7 лет назад

      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
      @chris-dd6uq 7 лет назад +1

      Maher Arora thank you for replying to my comments.

  • @bLittleHemi
    @bLittleHemi 9 лет назад +19

    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!

  • @Lu404Ai
    @Lu404Ai 2 года назад +1

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

  • @mimicmemento
    @mimicmemento 5 лет назад +1

    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!

  • @JoseOrtiz-dl5wc
    @JoseOrtiz-dl5wc 8 лет назад +7

    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.

  • @johnmwajinje1941
    @johnmwajinje1941 3 года назад +3

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

  • @seendidthegreat4814
    @seendidthegreat4814 5 месяцев назад

    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!

  • @vtecminileon
    @vtecminileon 8 лет назад +4

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

  • @virginiabushnell3042
    @virginiabushnell3042 5 лет назад +2

    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!

  • @Nonynonza
    @Nonynonza 7 лет назад

    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

  • @keroloskaras7973
    @keroloskaras7973 2 года назад

    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!!

  • @asiimwemicheal53
    @asiimwemicheal53 8 лет назад +16

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

  • @SeriZawa7743
    @SeriZawa7743 7 лет назад

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

  • @cr7neymar908
    @cr7neymar908 Год назад +3

    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

  • @georgesadler7830
    @georgesadler7830 Год назад

    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 RUclips. There are few errors in this playlist and they are corrected by the great viewers.

  • @dpmike32819
    @dpmike32819 3 года назад

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

  • @laforever401
    @laforever401 7 лет назад +8

    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!

  • @-AnweshaDas-
    @-AnweshaDas- 6 лет назад +11

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

  • @RedStormLax
    @RedStormLax 8 лет назад +1

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

  • @MisterFusion113
    @MisterFusion113 3 года назад

    This teacher is off the charts.

  • @henriqueoliveira3872
    @henriqueoliveira3872 Год назад

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

  • @andreaskoutsogiannis5795
    @andreaskoutsogiannis5795 8 лет назад +2

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

  • @Iz_moe
    @Iz_moe 2 года назад +1

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

  • @modesteakouete2473
    @modesteakouete2473 3 года назад

    i wouldve failed my class without your videos thanks Professor Leonard

  • @firohd8748
    @firohd8748 9 месяцев назад

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

  • @fatemehasgarinejad
    @fatemehasgarinejad 4 года назад

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

    • @beoptimistic5853
      @beoptimistic5853 3 года назад

      ruclips.net/video/fRyUf-GY754/видео.html .

  • @mashfique1
    @mashfique1 10 лет назад +1

    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....

  • @birincitekilsahs963
    @birincitekilsahs963 5 лет назад

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

  • @isaacroush2674
    @isaacroush2674 3 года назад +1

    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
      @beoptimistic5853 3 года назад

      ruclips.net/video/fRyUf-GY754/видео.html.

  • @siamtowhid3505
    @siamtowhid3505 9 лет назад +1

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

  • @petermiller5659
    @petermiller5659 9 лет назад

    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!!!

  • @vayneshade
    @vayneshade 7 лет назад

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

  • @muneebow
    @muneebow 9 лет назад +3

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

  • @FarisAlmaymani
    @FarisAlmaymani 9 лет назад

    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

  • @codewithmarwan
    @codewithmarwan 5 лет назад

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

  • @yazmingonzalez7965
    @yazmingonzalez7965 7 лет назад

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

  • @user-cl6yd2wk5j
    @user-cl6yd2wk5j 4 года назад +2

    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?

  • @ifahad4067
    @ifahad4067 10 лет назад +1

    the best math teacher ever .. thank you

  • @Heldawm
    @Heldawm 8 лет назад +5

    It was very clear.
    Thank you, from Brazil.

  • @xxsaifxx2450
    @xxsaifxx2450 7 месяцев назад

    bro without you i would fail engineering
    what a true legend

  • @dmanola7able
    @dmanola7able 7 лет назад

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

  • @ezeemmanuel7591
    @ezeemmanuel7591 3 года назад

    You are naturally born tutor.
    Subscribing already.👍🏻

  • @rosukiii.
    @rosukiii. 8 лет назад +1

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

  • @forexdailyearnings
    @forexdailyearnings 6 лет назад

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

  • @siyabulelamanona1438
    @siyabulelamanona1438 5 лет назад

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

  • @drinkgreen
    @drinkgreen 10 лет назад +3

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

  • @Ridgerunner2270
    @Ridgerunner2270 5 лет назад

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

  • @brightfutureacademy2323
    @brightfutureacademy2323 4 года назад

    بہت اچھے سر مجے آپ کی ویڈیو بہت پسند آئی ھے

  • @fatih.cevahir
    @fatih.cevahir 6 лет назад +2

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

  • @victorserras
    @victorserras 5 лет назад

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

  • @ducky2676
    @ducky2676 6 лет назад +2

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

  • @kirubelayele5734
    @kirubelayele5734 5 лет назад

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

  • @wealthoceans7348
    @wealthoceans7348 2 года назад

    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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  • @henri1_96
    @henri1_96 4 года назад

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

  • @alexandercervantes1078
    @alexandercervantes1078 5 лет назад

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

  • @adeolajoy4539
    @adeolajoy4539 7 месяцев назад

    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 😊

  • @matthewconsidine2492
    @matthewconsidine2492 10 месяцев назад +1

    Let’s make this guy a millionaire 🎉

  • @AnthonyGosal1452
    @AnthonyGosal1452 9 лет назад

    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!

  • @msjahun
    @msjahun 8 лет назад +1

    prof. you're a life saver.

  • @jeffreygomez7360
    @jeffreygomez7360 6 лет назад

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

  • @angel19955991
    @angel19955991 6 лет назад +1

    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

  • @donyagoodarzipour5720
    @donyagoodarzipour5720 4 года назад +1

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

    • @beoptimistic5853
      @beoptimistic5853 3 года назад

      ruclips.net/video/fRyUf-GY754/видео.html.

  • @fredanisi2364
    @fredanisi2364 9 лет назад +7

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

  • @EugeneWasSeen
    @EugeneWasSeen 8 лет назад +1

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

    • @greense65
      @greense65 8 лет назад

      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.

  • @girawatube2334
    @girawatube2334 6 лет назад

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

  • @TheAadiee
    @TheAadiee 9 лет назад +9

    Man, You so awesomely Handsome and great teacher!

  • @sangyaltsering7645
    @sangyaltsering7645 10 лет назад +2

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

  • @cinnamonspicelatte3124
    @cinnamonspicelatte3124 9 лет назад +2

    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!

  • @TheFunkyCriminal
    @TheFunkyCriminal 9 лет назад +2

    great lecture, definitely gonna keep watching

  • @fafiethamae
    @fafiethamae 2 месяца назад

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

  • @karikaranvetti4897
    @karikaranvetti4897 4 года назад

    i enjoy your lecture sir thanks a lot from SriLanka

  • @sameerrajput8732
    @sameerrajput8732 7 лет назад

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

  • @Chat2Conaz
    @Chat2Conaz 8 лет назад +1

    Thanks Professor! That was legit..... very well explained

  • @jyamijuice9100
    @jyamijuice9100 6 лет назад

    best math teacher

  • @mxkep
    @mxkep 7 лет назад

    Very helpful on my course in Numerical Methods. Thanks!

  • @iqmahoseni4268
    @iqmahoseni4268 3 года назад

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

  • @darimuhittin
    @darimuhittin 6 лет назад +1

    Beautiful explanation. Thank you sir.

  • @sadrazargarbashi3952
    @sadrazargarbashi3952 3 года назад

    جوون
    چه خوبی شما پروفسور

  • @mdazam5475
    @mdazam5475 8 лет назад +1

    thank u for the video. it's really help me to learn...trapezoidal & simpson rule...

  • @carl_yung
    @carl_yung 7 лет назад +1

    It's been a pleasure prof. i'll see you in calc 3 next semester :)

  • @FancySparrowGames
    @FancySparrowGames 9 лет назад +1

    Thank you this helped me to do a home work !

  • @martialway100
    @martialway100 10 лет назад +2

    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. :-)

  • @henrygarcia1152
    @henrygarcia1152 6 лет назад

    Prof Leonard is the man

  • @zahraarif7772
    @zahraarif7772 6 лет назад

    It was very helpful. You are the best! 😍

  • @mustafaRoya
    @mustafaRoya 8 лет назад +1

    Thank you so much professor Leonard

  • @ahmadnatour5221
    @ahmadnatour5221 9 лет назад +1

    love the lecture , very helpful very clear.

  • @mohamedriswan4854
    @mohamedriswan4854 3 года назад +1

    You are a lifesaver

    • @beoptimistic5853
      @beoptimistic5853 3 года назад +1

      ruclips.net/video/fRyUf-GY754/видео.html.

  • @MarkoVrbos
    @MarkoVrbos 2 года назад +1

    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