Simpson's Rule - Error Bound

[MARIOFREAK821]

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

[patrickJMT]

@MARIOFREAK821 the most famous hairy left arm of the internet

[franknguyen007]

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

[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 :(

[94suheyla]

thank u man :D I hope it will help me :))) thank u soooo much )))

[OpenTheTrollGate]

...one ring to bound them all...

[NguyenEmpir3]

Thanks alot, very helpful video, more helpful than my professor at least.

I never understood why mathematician created error bounds for trapezoids and midpoints rule when this method is much more accurate.

[patdarock]

thanks, I was trying to figure this out, but i didn't consider h= b-a/n so I wasn't able to get n LOL.

[1Man2Go]

i love you

[KONIXMUSIC]

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

[macabrebunny]

I love the USA.

[patrickJMT]

@macabrebunny i rather like it myself

[macabrebunny]

@patrickJMT I know! Can you guys believe this?! Free Maths?!

[ShrodingersPerson]

i cant say thank you enough.

[TheOblivionGate]

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.

[pullan735]

do you always take it to the 4th root? or does it vary?

thanks

[NguyenEmpir3]

@pullan735 you take 4th root on both sides because you have n to the 4th power.

[0060129046346]

sir! why not n=18 ??

[ShrodingersPerson]

@0060129046346 because it has to be greater than or equal to 18.4. 18 is less :D

[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!

[jlap1010]

I am just wondering why my textbook says only second derivative is required? is it because its using simpson's? whereas my textbook uses trapezoid or midpoint's?

[jlap1010]

I am just wondering why my textbook says only second derivative is required?

[AznLonelyBoi]

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

[BridgidK]

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

[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!

[lifethroughmylens1]

Funny funny funny I love it. Can you draw my dog.

[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.

[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]

@Therizah2 good luck!! :  )

[hbobbomb]

Why aren't you my maths teacher?!

[patrickJMT]

@hbobbomb i guess cause i do not teach : )

[ri394]

this beats reading a textbook. i'm just gonna come here for all my calc question

[alikhan1414]

thank u for uploading this

[MetallicAus]

(b-a)^5 Patrick 

[patrickJMT]

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

[MRclownface123]

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

[kateeeeex0]

i watched about 20 of your videos.. most of them more then once. i have a calculus exam tomorrow and was honestly probably going to bomb it until i watched these videos. my brain hurts but honestly it's so worth it. THANK YOU!

[009overlord]

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

[peiznkev000]

I JUST now noticed you're left handed...like me! :D

[simon42o]

THank you <3



[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!

[cjfost]

What happened to the e? How do you do that equation?

[darkman8803]

@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.

[lilangel0072]

@darkman8803 a 57.9 average is considered a B+.....jesus...where do u go to school to, sign me up.

[VirusMaximus]

Sir, you are awesome at explaining things.

[vitaminwater2221]

hmm shoud k(b-a) be k(b-a)^5 at 8:52...

[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

[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.

[empyrionin]

@mahzkrieg Like vitaminwater221 pointed out you have the wrong error bounds formula, you have a Es = k(b-a) / 180n^4 when you should have Es = k(b-a)^5 / 180n^4, notice the fifth power there for (b-a). Luckily for the result, in this video (b-a) is equal to (b-a)^5 since it's 1.

[JLarry09]

@mahzkrieg you are absolutley right. I had a crazy teacher who DEMONIZEZ math. He took this simpsons rule and made it more difficult than anything you can imagine.

Kudos to you patrickJMT you are 100 better than 90% of college professors out there. keep it up

[clickthebutton]

you are a genius!!! thank you so much for your help! i was so confused but after watching your example the problem makes perfect sense!

[etothebang]

patrick u are a fucking angel. i just want to say thank you so much. ur videos help me so much. my cal II teacher cant explain this material no where near as clear as u do. So i wanna say thank you so much. and please dont let these internet fags that are always leaving negative comments get to you. u are helping people in a epic way.

[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. :)

[Wyndrax]

Really interesting.

[4thKyuubi]

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

[4thKyuubi]

I dont get how you solve for k, what do you do to get it

[4thKyuubi]

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

[4thKyuubi]

@4thKyuubi please please please anyone, i need this hw before 12 midnight tonight. What do you do to solve for K here? Anyone?

[jeffryder9]

THANK YOU!!! this helped a lot !

[ddkramerful]

patrick..no matter what anyone says..you are helping SO many people by taking your own time out to make these videos and present calculus in an understandable, clear, applicable way. everyone who has ever watched one of your videos should be donating money.

[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...

[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 =)

[xoMissMeliss]

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

[Millenx]

I am going to ace this class thanks to you!

[Stags209]

to jianjaneyang: you wouldnt need to do simpsons rule for that because u can find the exact value using the fundamental theorem of calc. simpsons rule is for approximating unintegrable problems.

[jianjaneyang]

how would you do something like finding error bound using Simpson's rule with integral (x^2 + 1) dx from -1 to 1? i tried to find the fourth derivative , i don't think that is possible!

[hkpopfan4lif3]

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

[hotarujj1]

Thanks! This is a great explanation.

[confederateblood]

I believe at 8.17 when writing error bound formula, forgot to write (b-a)^5. you wrote (b-a). so ???

[matinaeau]

I think he just forgot it but it should be raised to the power of 5. Because the value that need to be raised to 5 was 1 for this example, it still worked out.

[sellingcauses]

it is (b-a)^5

however, in the example (1-0)^5 = 1 so it doesnt matter

[HD5750]

I noticed that too...I was gonna point it..but then saw your comment... :)

[alistan91]

yea cause his b-a was 1 so doesnt matter bout ^5

[rogelioh09]

You are seriously good at explaining and following thru. Very impressive

[fatvegas9]

How do you estimate the error in A2, the '2 piece' composite Simpson's rule?

[tonymac96]

I'm asking my student to go an check your videos. If they miss something...you probably will cover it.

Thanks.

[3132029]

thank u so much! im passing cal 2 with and A because of ur videos! ur awesome man!

[xxxbakirxxx]

god bless u!

[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.

[mlgcool]

Great Video!! Thanks for all of the help!!

[Kenjineering]

What would be icing on the cake... are a video series on proofs :S

[patrickJMT]

no one ever cares about proofs though...

[Kenjineering]

"no one ever cares about proofs though... "

really? lecturers? students? youtube audience? everyone?

My examinations usually ask for several proofs.

[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?

[tehretardedbunny]

@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!

[Kenjineering]

@tehretardedbunny Yes I was vague, I was busy and forgot to come back and explain myself. From memory, what I was hinting at were derivations of common engineering equations such as umm... bernoulli, RANS, Airy Stress Functions, Boundary layer equations...etc.. Either derivations or the physical interpretation of terms.

[Kenjineering]

"..how about you try making a 'video series' ..." blah blah

Are you being a sarcastic smart arse here? If so, remember this is a channel of learning and that questions, no matter how munted or vague, should be welcomed. Questions, in my mind, provoke nothing but value adding discussion. In your mind it is evident, from that quote, that they are to be treated with petty on the sly remarks. I'm going to have to block you now.

[Kenjineering]

I was just thinking the other day.. students ALWAYS explain things better than lectures (they know where you might trip up), and I was thinking that when I graduate from engineering, I am going to make a whole series of videos that are going to save fellow maths students from the frustration of vague explanations. BUT I DONT HAVE TO ANYMORE!! CHEERS!!

[Dehar]

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

[lookitscorky]

this is awesome! thanks :D

[gambuzo]

Question about n - what is it ? Is it the number of intervals or the number of poins between a and b ?

I'm a bit confused.

[MeshRoun]

number of intervals

[weezyanasupafly]

why did he take the 4th derivative of the function?

[nappyxnelson]

the formula asks for it. in the beginning F^4 is less than or equal to K. but if your looking at midpoint or trapezoid error bounds it takes F^2 less than or equal to K

[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

[karen1983il]

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

[patrickJMT]

you are boring

[eclipx]

you better shut the fuck up

[patrickJMT]

nah, i don't think i will.

i mean, at least make a 'non-boring' comment. otherwise, you just look like a dumb ho, ya dig?

[gellybelly2]

Woops, Sorry, it's because 1^5, is 1 anyway.

[patrickJMT]

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

[gellybelly2]

I don't understand why it isn't (b-a)^5?

[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.

[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]

i am not sure i understand your question...