Simpson's Rule - Error Bound

[@benjaminaho]

I always go to this video to see how to calculate K. EVERYWHERE just expects you to know how except for this video. Thank you!

[@patrickjmt]

Benny A glad i could help! come back anytime ;)

[@jfhowlpendragon]

You have shed light on an area of calculus that had me in almost tears because I had no idea what my lecturer was talking about for 6 hours. >.< You have explained it in simply 11 minutes. Kudos and thanks. :)

[@jessicathompson4979]

This video was a life saver!!! Have a test in less than 24 hours and you've explained this better than my professor has for the past 2 weeks. Thank you so much!!

[@ientonghien5941]

Jessica Thompson beacause you are stupid XD

[@chriscastromd]

CALC II TEST tomorrow. about to go HAM... my all nighter will not be as bad thanks to u!!!!

[@MaddiAl-n7o]

literally the best use of my time and fantastic explaining, really loved this tutorial 15 years later thanks a ton man

[@voidzilla]

I think I could kiss you right about now! Between you, Sal Khan, Numericalmethodsguy and Gilbert Strang (MIT) there's genius an order of magnitude. Its not even what you guys know (which is impressive by any standard), rather its how well you communicate it across. I'm a Comsci/Maths major and I think I'd have failed without you all. YOU ROCK PatrickJMT!

[@emmyisamerican]

Using your videos I managed my first 94% on my Calculus midterm- Thank you so much.

[@jjsc5986]

u graduated yet lmao 🤓

[@gabyrosey]

thank you so much for explaining how to find K!! literally no where in the chapter of my book showed me how to do it

[@1RealAzul]

You sir have made everything so clear. If only I had watched this video before submitting my homework, but the good thing is I know how to do this now which should help me prepare for my quiz on Friday.

[@jeffjazzy6189]

Thanks a lot Patrick JMT you videos really assist me in to simplify most of the stuff when it comes to calculus. You are doing a great job.

[@seggyRK]

you forgot to raise the (b-a)^5 towards the ending but no biggie, answer was still correct. Excellent video!

[@patrickjmt]

thanks mr. einstein. that means a lot coming from you!

[@DeneuveBrutus]

@mahzkrieg I aggree, I recently started watching these videos last week I found it fumbling on the internet looking for the" reason to integrate by parts".... and "when to use partial fractions" I watched TWO videos and I understood the concept I never practiced a problem because it was 3 clock in the morning and the test was at 9. Needles to say, those video helped me accrue more than 30 points on the exam, with a class avg. of 57.9 which is a B+, i received a 50.. I am truly grateful.

[@Leetky]

Yo, you are my man! I was too confused with doing this simpson rule problem so I search for simpsons rule and long behold you do the same exact question I have for 1 of my HW questions. Thank You so much. I'm gonna subscribe you.

[@mahzkrieg]

it's unfortunate that schools/universities glorify hard teachers while the good teachers that can break down initially complex-looking problems are reserved for community colleges and "level" students. the only thing that makes a math educator hard is his or her inability to communicate the concepts in an intuitive manner to students. your videos helped me supplement a ridiculously hard university calc course with class exam averages in the 30s. yet you should be the one that receives my tuition

[@dhpgoalie]

I think it's more of a question of the difficulty of the course. I know what you mean. My physics class just averaged 38 on the last exam. But I don't feel this was due to a lack of clear explanation on my professor's part. The exam was just incredibly difficult. He explained that we can't expect to get 90's like we did in high school. In life, success is all relative. I do feel some professors could explain better, but i don't feel com. col. has superior educators. They are there for a reason.

[@DashofDosh]

Where were you during my ap exam???! Probably waiting for me to get my 4 and then come running to you for Calc 2 :D Thanks!

[@schang_lh]

thank you, this was very helpful! @10:51 I was stuck up on a question as to why my prof round a 21.4 to 22 until I saw ur video and was reminded that simpon's rule only take even 'n' value. Thank You!

[@MrItsninja]

It's just part of the error bound formula/method for simpsons rule. If you do the error bound for the trapezoid rule for example, it requires that you take the second derivative.

[@Miguel-ng5wm]

You are like the best teacher on youtube! thanks!

[@rikimay]

Damn! i am from Spain and thanks to you i am learning a lot! You explanations are good and clear. From now on u will become my teacher! Awesome dude!

[@009overlord]

thank you, you are doing a great service to humanity.

[@patrickjmt]

well, most people are not interested in proofs is what i really mean. do you mean videos on different proof techniques (induction, contradiction, etc) or simply proofs of the different calc results?

[@holycowrap]

You explained this alot better than my calculus book! Thank you!

[@patrickjmt]

thanks for the kind words ;)

[@patrickjmt]

@mahzkrieg glad i was able to help. the top researchers bring in bring grant money from the nsf, and this is what universities want. if you happen to be able to teach a person or two, then good for you.... of course, there are many great researchers who are also great professors (akram aldroubi at vanderbilt was one person i met who did both very well), but in my experience, they seem to be the exception instead of the rule.

[@LoveHateSerendipity]

Hopefully all of the Patrickjmt vids I've been watching last week to now, pay off this Thursday. Dun dun--onward!

[@BridgidK]

Thank you for the videos. They are a great refresher prior to my finals in numerical analysis.

[@sn0wchyld]

because trapazoidal rule is generally 'less accurate' than simpsons. simpons is a combination of trap and 'midpoint' rules, i think... but basically because simp. takes more reference points than trap, its inherently more accurate. sorry if thats not totally clear, im still learning this shit myself.

[@patrickjmt]

@MetallicAus i put some annotations in there that it should still be raised to the 5th power! thanks.

[@ChrisBonJovi]

And the mysterious, floating, hairy arm has saved the day again. Thanks!

[@georgetallah6254]

Thanks so much. The video is Really helpful. Besides, I noticed that you never raise (b-a) to the fifth power. Of course when one is raise to power 5 is just one. You'd have just indicated it , my classmate strongly argued with me that the formula doesn't have any value raised to power 5 which is not true. 😂😂. Thanks once again 🙏🙏.

[@Jankin47]

You sir, teach far better than my fossilized math teacher.

[@thedrumman64]

Another excellent video, as always. :-) Just one question however. At the 9:20 mark, why is it not written as '0.00001 is less than or equal to (76e/180n^4)? Did the inequality become reversed somehow?

[@WolvesOfAtlantis]

Simpson's rule is essentially calculating a curve fit for each n, whereas trapezoidal rule can't balance over and under approximations. (I know this is a a bit late.)

[@timmistarr9800]

Loved this one.Thanks patrick!

[@sharma1337]

Thanks patrick for making it clearer than the book. One question it says in the book "K can be any number larger then the abs if f^4 derivative but smaller k usually gives tighter error bounds" If we wanted the smallest error than we need the smallest K using the a

[@patrickjmt]

@ddkramerful well, most people seem to appreciate them : ) given that this is the internet and that i only rarely receive a negative comment is nothing less than miraculous to me...

[@GeorgeChen]

At 9:12, the sides of the inequality are flipped, so shouldn't the sign be flipped as "greater than and equal to"?

[@ivanljujic4128]

8 years later, still no answer. I found other videos with the EXACT SAME MISTAKE. It makes sense that it would give tou the lower limit for n, right? Like N has to be above, for example, 10 so your approximation is more accurate. Anyway I doubt you'll have the use for it 8 years later but I had to respond XD

[@MRclownface123]

i wish you were my professor, it would make calc 2 a whole lot better!

[@MoreKevinLiang]

this exact problem is in my math textbook for homework lol I got stuck on it...so I consulted here. Awesome

[@pojhugygfgv]

This makes much more sense then my book. Also, the first ever question I had to do in my class for error in a Simpsons approximation wasn't an e to the x squared or a sin(3x). It was a fucking cos(200(pi)x). The god damned max for the 4th derivative of that is 16 billion multiplied by pi to the 4th power. Seriously?

[@Therizah2]

Hope this helps me with my maths investo verification test tomorrow, only time will find out!!!! Wish me and my class luck!! Thanks :D

[@patrickjmt]

@MARIOFREAK821 the most famous hairy left arm of the internet

[@Claugustus]

Thank you Patrick! I agree with what Benny said, not even my textbook says how to get K! How am I supposed to just know? I don't! Thanks!

[@DarkWolf887]

Still working after the 2021 update

[@alikhan1414]

thank u for uploading this

[@KONIXMUSIC]

I know its going to be a hard section when I can't even follow your videos.

[@kathyoh5272]

im a bit confused. where does the 180 come from? my textbook shows that the formula for simpon's rule error is -(b-a)^5/[2880(n^4)] times f^(4)(c).

[@xoMissMeliss]

you can factor out the 4th derivative even more.. (4e^x^2)(3 + 12x^2 +4x^4) ... just saying.. But thank you sooooooooo mcuh! i understand now =)

[@JayRileyArgue]

Excellent work

[@patrickjmt]

no problem :)

[@pranavthirumalai126]

The first equation that you show us, is that a general formula? If so, where does the 180 come from? Thank you so much for your help!

[@64salvador64]

Thank you! Omg! Mind blown... So needed to know all this for test

[@Rose-ek2yc]

Same

[@patrickjmt]

i am not sure i understand your question...

[@sheenapak]

isn't the approximation supposed to be close to 0.0001, and not 0.00001? Because that's what my calc. book says and if u use 0.0001, you get different answer than 0.00001. Also when you were substituing all the value in the equation, wasn't is supposed to be 76e(1)^5 in numerator and not just 76e(1)? I know it doesnt matter in this case, but just wanted to point out.

[@mohd1210]

there was an ad at the beginning, middle and end of the video. I didn't mind em since i like youtube being free but three ads per video? not cool.

[@patrickjmt]

yep, exactly! i just 'cut to the chase'

[@por2gee123isGAY]

@patrickJMT when finding the value of K, are you trying to maximize the value of the 4th derivative, or maximize the value of the absolute value of the 4th derivative?

[@FreeSeoul]

Why is it 180n^4? Where does that value come from? I know where the top values come from but the bottom seems just like a random luck plot.

[@tehfunnybunny]

@Kenjineering Can you be any more vague about 'proofs'? Lol I mean, how about you try making a 'video series' with about hundred different videos on 'proofs'. I mean, that would Really be the icing on the cake!

[@cachdoan]

Patrick, when you apply the formula of the error bound for simpson rule, you didnt put the 5th power on (b-a). I assume you ignor it since the value inside is 1.

[@sadafnoreen841]

Thank you so much . it helps me a lot

[@joshjr1209]

ty patrick u save my final

[@sicktoaster]

Is there a way to figure out an error bound when the function isn't given, but instead there is a line going through points? And what about for the trapezoidal rule or Reimann sums?

[@franknguyen007]

I wish my profs just put your vid on his lecture, which would be more effective.

[@karen1983il]

how can i find how large 'n' should be to ensure that the trapezoidal rule approximation to some integral is accurate to w/in 0.00001

[@TheStrongAdam]

This was very helpful, thank you!

[@jeffryder9]

THANK YOU!!! this helped a lot !

[@BreadedRedhead]

beautiful handwriting

[@Ihatenicknames1]

Thank you for the help! :)

[@isaaclinn2954]

Maybe invest in a larger whiteboard? Great video!

[@patrickjmt]

@hbobbomb i guess cause i do not teach : )

[@AdmCornFlake]

Thanks a lot! This was really helpful!

[@xoMissMeliss]

you can factor out the 4th derivative even more.. (4e^x^2)(3 + 12x^2 +4x^4) ... just saying

[@ankit87gupta123]

Is this formula for Simpson's 1/3 rd rule or (3/8) rule?

[@srayastammineni6557]

Gud work Man !!! U did well !! Gud Job... go a Head My Boy.

[@sicktoaster]

8:22 Don't you also have to subtract f(4) (0) from it? Since e^0=1 that would be 12.

[@94suheyla]

thank u 4 dis vid. sooooooo much :) but can u plz tell me what did u write at the beginnig of the video?I can't read the words :(

[@adubashi]

Do you always need to find the fourth derivative for simpsons rule? Or could it possibly be the 2nd or 3rd derivative?

[@4thKyuubi]

Isnt the quantity of (b-a) should be to the 5th power? For the formula for the error bound of simpson rule?

[@IpN0oTiC]

Very usefull. Nice video!! Thank you very much

[@safiresafire1]

Do you always find the maximum for error bound problems in the same way (plugging the bounds into the given derivative to see which is bigger)? Thanks!

[@BlackfireGippal]

i don't get it why the error bound calculated with trapezoidal rule isn't equal to the one calculated with Simpson's rule

[@wkcacc]

What does the JMT of patrick JMT stand for?

[@jenevxn]

thx for wonderful work"big fan" but i have a question what if it was17 should we change it to 18

[@4thKyuubi]

So basically, you always plug in the upper bound into the function to get K?

[@84brex84]

Thank u so much from italy

[@karen1983il]

great video.... helped me alot... thanks

[@adzplus1]

can you use simpson's rule to find the approximation of the definite integral of any function? and which one is more simpler and better for the approximation of definite integrals: taylor series or simpson's rule? I want to know this because there are some functions that cannot be integrated such as the one in this video. regards

[@mgofthefc]

how come elsewhere on the internet I have seen the numerator written as K(b-a)^5 ? Did you just leave off that 5th power because for this particular equation 1^5 = 1 ?

[@ZarinaZinaZ]

You are the best thing that's ever happened to me

[@Cenedra-o9c]

thanks so much it eas a pretty clear explanation on how to find K

[@TofuCate]

@jlap1010 This is reffering to the simpsons rule. The formula is a bit different when dealing with trapezoids and midpoints.

[@lizziewills1237]

You are my amazing savior!!!

[@jvaferreira93]

Do I always need to derivate that equation or is it the one I'm working with?

[@fR4G]

i remember doing this in my numerical methods class. i was wondering if this applies to both 1/3 and 3/8 simpsons?

[@patrickjmt]

@Therizah2 good luck!! : )

[@lomakak]

When finding the error bounds my lecturer doesn't have a-b to the power of 5 and also there is no n^-4 but h^4 instead (h being the step increase from a to b). Can someone explain if there is a difference?

[@Dehar]

I think you forgot to do (b-a)^5 at that end of the problem.....