Calculus 1.1: Functions

[bebeheuy]

I am very happy to see the vidoe after you give this The first section in the Calculus I sequence. We cover the definition of a function, its domain and range, and how functions might be used in calculus.

[AntoMelta]

I Really Like The Video From Your The first section in the Calculus I sequence. We cover the definition of a function, its domain and range, and how functions might be used in calculus

[willamricard]

Your Video Is Very Useful Sharing The first section in the Calculus I sequence. We cover the definition of a function, its domain and range, and how functions might be used in calculus.

[imegatrone]

after i watched this video, my insight is very open because the video is very good to give information The first section in the Calculus I sequence. We cover the definition of a function, its domain and range, and how functions might be used in calculus.

[winaproduction]

nice audio fucktard!

[hellloooari]

I swear... This has cleared up years worth of my mathematical confusion. This dude makes for a great teacher.

[VKM7md]

Thank u so much! I studied Calculus in Arabic and this helped a lot in translating the terms.

[PAKlSTANl]

is this a radio learning?!

[ZipperHead31]

Nobody wants math oh "YouTube".... There'd a site called teachertube you know...

[DudMan2111]

@ZipperHead31 speak for yourself...please

[BalladoftheWindfish]

I just started watching these today. I hope they will supplement my learning. Thank you so much for putting these up!

[shmuli9]

It's said quite often that "a function has to have a unique value in the X-direction, and therefore equations where an "x" is defined as the same value for two different values of "y" is not a function".  Do mathematicians ever more or less flip the "x" and "y" scales 90 degrees and use the transformed function to find the area "under" the cuve?

[DartmouthAlum96]

Mathematics is a banal waste of time. The only worthwhile academic discipline is ethno-Chicano-African-Womyn's-­American studies.

[niggbreaker]

excellent! thank you, very good logic

[jaigooroo]

I learned functions in college algebra. wierd.

[trinidadisthebest12]

following the british system we donot really call it calculus, but its pretty much the same, soome slight changes, and we learn other things like binomials etc, dunno if thats also in calculus,

[robloxgaara22]

Im a 7th grader trying to learn calculus and I think it made since in mybrain , but Ill think Ill just stick with finding Square roots without a calculator and I'll learn this stuff later on...

[shmuli9]

@robloxgaara22 I found that if you step back from it, calculus actually makes intuitive sense, but when immersed in "limits" and "Riemann sums" and the like, it becomes kind of esoteric.

[wenaolong]

That should have been "X-(round)X", not "(round)X-X", shouldn't've?

[wenaolong]

I know the function for psychologically "seeing" fourth dimensional objects constantly on a moment-to-moment basis, and this can include rather large "landmark"-type four-dimensional objects.

[bomberfun1]

You are extremely rushing. You are repeating, not teaching.

[TheImmigrantsong]

I learned all of calculus and now i understood what function is :D

[raist2]

Great video, keep it up.

[ocsvcsvcsvo]

is this really the beginning of calculus? i learned this in intermediate algebra

[partygreens1]

basis of calculus is functions.. IF functions are not clear, calculus won't be either.. So, it's necessary to understand this.

[freejdc1]

thats why its the beginning

[unemployedforever]

does anybody know how to simplify this for the retards who flew by through highschool with all d's

[JazzyTee89]

Good job! You teach better than my professor

[thelostgirl1313]

this is fabulous for reviewing stuff... you are awesome XD

[mokvid]

everything is perfect but dont erase the board so quick, im taking notes :)

[mattiieeeee]

or maybe you could pause.

just sayin'

[Tamlin2308]

Pause the Video, Dumbfuck.

[bacofishtaco]

You made me understand this perfectly, and I'm in 9th grade Algebra.

[classicmusic05]

grade 9? soft

everything in this video is like grade 7

[smkk1000]

the book made me carzy but ved made it easy thanks again

[beyondastars]

thanks soo much :D

[dnd2011]

I LOVE U THANK YOU!!!

[mobsterli]

awsome. thanks for this :)

[navly]

explained to perfection

[chile1231]

good fast review.

[aja978]

thanks for the video !

anyone who is interested to practice solving calculus problems may also find the book "Calculus Workbook for Dummies" useful. it focuses on helping you solve the many types of calculus problems

selfservingbooks (.) com/dummies/Calculus-Workbook-­Dummies-Mark-Ryan/1742

[replace (.) with . ]

[dnd2011]

thanks

[Bera1989]

COOOOOL!! (Y)

[Liene37]

thaaaanx , Understood! :D

[MoonMaidMokona]

Thank you so much, having a test tomorrow and this is excellent recap :D

[PLA5T1KJ3ZUS]

ive been taking notes from these videos cuz im not very good at my math put i need to take calculus to help with me game development. so mainly i use these videos as sumthin to help transition

[7ether]

It is very that I want!

[k1ngross]

Useful, thanks

[funkadalik]

thank you so much

[all22787]

Thanks

[arphamdb]

This is still okay for me, I'm new to Calculus. I only don't understand what's round(x). Could someone please explain to me?

[terranfighte1]

Round(x) is just apart of the function. 0 isn't allowed so no integers are allowed for x, meaning that x can be 2.3 but not 2; or it can be 7.23232234234, but not 7 because you cannot divide by 0. Considering the forumula 1/(round(x)) - X If you give the value 7.23232234234 to X then the forumula goes as followed =1/(round(7.23232234234) - 7.23232234234) =1/ 7 - 7.23232234234 =1/ 0.23232234234 =4.3 (ans was rounded to the tenth) if f(x)->Y, x=7 then =1/(round(7)-7) =1/(7-) =1/0 =undefined

[HookMe10]

well said terranfighte1. thanks

[rapmastrd3502]

it confused me even more

[zwienerrocks]

OK...I GET IT NOW.

=]

[sanshuz]

Hey complicate as much as ya can. Ya haven't got a clue how to teach.

[bomberfun1]

@sanshuz agree 100%

[estringfellow]

i could do this problem in dark and be finished and he would still be explaining functions

[Silverhailo21]

I'm teaching myself Calc, and I can't thank you enough sir for your tutelage. Just wanted to let you know what you've really helped a serious student out. (I'm trying to move on to some more complicated math to better understand String and M Theory.) :)

[warlock1276]

calculus is a little complicated but doable

[estringfellow]

This is horrible. Making things waaay too complicated.I teach calculus and I am falling asleep.

[Dedboy43]

i am 14 years old and i am taking AB calculus

i think this is a discrete way of explaining fuctions, though effective and smart nonetheless.

[cougarbart]

Actually your name tag says you're 25.

[ish718]

LOL

[xiner]

No one would make fun of a reading lesson. Sad Americans.

[xantares13]

um you're profile says your from america

[bdtdot]

holy math

[daganboy]

Isn't this in precalculus?

-Dagan, 14

[Beefstew2011]

Daganboy, it probably was in a pre-calc course however its just section 1.1 so it's probably more of a review.

[ProgrammedDamned]

hahaha lol nice 1

[Boddingtons1]

I don't even think people who build bridges really need this stuff. they only need a few simple-to-understand principles of physics and elementary mathematics. Unfair to me that lack of being able to follow this kinda shit is going to affect some poor student's self-esteem because he/she is not "smart enough" Cause I don't know what this guy is talking about. But I also don't care!

[jeraldinys]

um...to build a bridge, you need to more than simple physics and you need some pretty high level math. You'll understand more when you take AP Calculus BC (or AB) and Physics C. If you don't understand what this guy is talking about...maybe it's cuz he's not that great? Once you get a real teacher that you can actually talk to, you'll start to understand more.

[Boddingtons1]

I guess you're right. It's just frustrating to be a victim of a perpetual lack of understanding. My wife is excellent at math and says most teachers have no idea how to explain this stuff in any way other than the one they were taught and that's why History majors like me get frustrated; because it makes math come off like this strict, unforgiving and completely non-intuitive, rote discipline that could never ever be interesting or fun.

[xantares13]

i'm not asking this to be rude but what do you do with a history major?

i have a friend who's going to college this year to major in history and I think it's important to know at least some of what's happened but what exactly do history majors do?

[RocknRollDina]

i always wonder the same thing also. I'm guessing they teach or/and do researches.

[mai2xs]

I was thinking about it the other day, why would you pay 20, 30, 40 thousands in an history degree when you can simply go to Wikipedia and learn just as much.

[xantares13]

would you actually go learn that much stuff and would you hire someone who went to wiki instead of college?

i get your point though

[edthehustler]

because anyone can go to wikipedia and change any article on there, which means you wont learn anything, which then means you would end up in college to learn.

[jasonguyperson]

historian, record keeper, high school teacher, college professor, researcher...

[mingalabaa]

Wiki info is reliable for Science info only.

[Boddingtons1]

You can work as a consultant on films, documentaries and TV shows about historical subjects. You can work for museums. You can consult for the federal government or the military. And if you want to be a writer of compelling drama, stage, screen or otherwise, you can find no better inspiration than in the pages of history. Some of the best-loved films in history contain allusions or direct parallels to historical events and put them out there in modern dress so we don't repeat the mistakes.

[rleroygordon]

Don't feel bad. I've taken Calc. I have a fairly decent handle on it (finally!). But this guy is doing a terrible job of explaining functions.

[Boddingtons1]

Yeah, but I'm thirty years old. Something should have cracked by now. My wife tutors me but...oh well, you get nothing without struggling, right? I'll just have to keep studying. Thanks.

[rleroygordon]

And I'm 56 (sob!). I pulled a C+ in Calc I back in '77 (I was 25). Repeated it in 2000. Left a smokin' hole in the ground. That wasn't the point. I'd just finished Precalc with an A the semester before. My Calc instructor spent the requisite first week of review. I swear that after he finished covering functions, even _I_ couldn't understand the subject. It went downhill from there.

[shadowlink96]

Umm, this is pretty easy to follow actually

[barryokonoboh]

A function is a set of ordered pairs in which no two distinct pairs have the same first element.

[irvpat]

I love calculus!

[busrider85]

A function is map in which an element e in set x corresponds to one and only one element f in set y.

[Aro2220]

Honestly, if you don't want to learn things then don't. If you do, then do.

But, there's no point to you posting that you don't care about something. Just move on with your life...

[autobahnguy]

I'm 20 and starting to learn this material for the first time.

[NoseEverything]

This video explains very basic stuff in a very complicated way.

[fantasydemon360]

I know right alot in the begining was basic algebra

[jgall502]

I can count up to 28 empty beer cans but then I seem to get confused.

[JeffThunder]

i don't even know how to add money how am i sposed to know this shit

[jgall502]

I can barely calculate how much change I'll be getting back from a 12 pack of beer this calculus crap is Greek to me.

[deazn1]

Wow, you just proved to me why I shouldn't respond to any of your retard comments. Plz just learn subtraction first. Possibly even go to college.

[jgall502]

College? I ain't smart 'nuff fo' high school.

[jgall502]

Do blue collar people even need to know algebra, let alone calculus?

[Tangerinemustang]

time to go to sleep for me so ill watch this video

[deazn1]

wow, this is fucking stupid. Wasted 2 minutes of my life. Everyone should already know this stuff.

[jgall502]

/////wow, this is fucking stupid. Wasted 2 minutes of my life. Everyone should already know this stuff.///// ---Everyone should know what an a**hole you are.

[Jarmanz4]

im left handed too. YeAHHH!!!!!

[naruto51XX]

me too!!!! hi-5! lol

[blkjedi954]

this sucks!!

[slimshadygabino]

how does calculus help you in life?

[PooFetish]

Good point, how does calculus help in life? I never got a straight answer from my teachers.

[kelvinhbo]

differential calculus is used to measure change in equations for example if you are doing an experiment and you want to know what would've happened if you did the experiment for a longer time, change forces etc. Integral calculus is used to measure the consequences of change in equations.

[Phranquely]

Calculus is responsible for the computer you are typing on. That is one way it helps in life.

[yasamih]

what r u talking about?

[Phranquely]

My comment is pretty self explanatory...

[Xearf]

Well today, Calculus helped me put together a box with a maximized volume. XD

How that box helped me in life, I'll never know; it's good for companies who want to maximize profit and minimize cost, though. Anyhow, that's just one aspect of Calculus that we happen to be going over in school right now.

[Jersangg]

it might not help you directly with an everyday task, or even common non-everyday tasks, but its concepts fuel technology and fuel science.

without calculus we would not be enjoying some of the fine technologies that we do today.

but whats more, the concepts help your brain expand, it opens up mental pathways which ultimately makes you smarter, and whether you see no physical result from that, you are then smarter and your life will be just that much better....

[yasamih]

but it doesn't help me to see my opened up mental pathways physicaly, so how do i know whether it opened them up or not, im confused!

[Jersangg]

you cant "physically" see how your brain is improving, but i gaurantee that by practising difficult concepts your brain grows and adapts and learns, and you become smarter out of it, thats simply all. it takes practise and dedication and is not for everyone, but if you do take it that is what it will do for you

[EuterpeOapin]

Actually i remember a National Geographic article I read last year that did a study of the human brain on a taxi driver, what was the astounding part of it was that, allthough he was in his 30's the section of the brain that delt with spacial memory. What he needed to remeber the town, was quite overdeveloped, to a great extent. So allthough your brain might be "wired" completely, this doesn't mean it doesn't quit growing and adapting.

[hereisthankappan]

wow that sounds great ...where exactly did ya find the research ...

ty

[jenyu888]

Calculus helped me get a job paying $92K right out of college :)

[slimshadygabino]

what job is that?

[4EVAORLANDO]

wot the fuck uis calculus

[sketchy0788]

you're a very good instructor, are you a real life teacher? if not, go for it.

[bradkey98765]

hmm, well i'm 15 and and all i'm doing at school on calculus is, integration (anti-derivatives) and differentiation. So where doing quite a bit of curve sketching with cubic graphs, and area under the curve.... which is starting to get rather easy, we haven't looked at functions yet so this learnt me quite a bit.

Best of luck for your other videos.

[sqnshl]

jesus your 15 and your learning integration!?! Is it me or Australia's schools are a tad slow, we learned to that in year 12 :( (unless your on an Extension 2 maths class in year 9-10?)

[yasamih]

well we do all calculus classes in high school. no calculus in college, but english termonology makes it difficult.

[raulaassis]

Man, please correct some of your mistakes. For f:X-> Y to be a function, ALL elements in X must be associated with only one element in Y. In your first example 7 is left out, then f is not a function. See, there ara 2 conditions for f to be a funtion:

a) ALL elements in X must be associated with some element in Y

b) each element associates to only ONE element in Y.

This same mistake is repeated over and over again in your examples.

Good initiative though.

[purplecucumber18]

i write my 7s like that too

nice vid 8)

[madchild123]

FYI math is calculus... or is calculus, math? I could pretty well argue both sides..

Anyhow, interesting concepts for an introduction to functions. I prefer the brute force method of explain math and it's idealistic concepts--not so many metaphors and what not.

Good job!

[2terence2jones]

FYI, this is math...

[GVDTWOTS]

this is algebra...

[zaindy87]

Good intro to functions.

[CeerigaBoSomalia]

LOOL DOMAIN FOR X square is positive infinity to positive infinity. chek it when u graph it.

[ChoujiAkimichi]

Domain refers to the X!!!!! component. In case you have forgotten it is the HORIZONTAL line (the one that goes left to right).

it is from NEGATIVE infinity to POSITIVE infinity.

Also, infinity is a concept! not a number. there is no such thing as a domain from positive infinity to positive infinity because if you say that then the domain only has one point. But infinity is not defined because it is a concept.

[NZLAD123]

thanks man this is great help

[fireken5]

what is a derivative (lol copy and pasted that last word from some persons comment)

[vanhalenmk]

great video. i love mathematics, and want to learn as much of it as possible.

is there any absolutley amazing mathematics books i can read???

[hanshv]

Check this Out William Anthony Granville The Calculus , Louis Leithold TC7 there are for high level

[photografr7]

In the simplest case, the first derivative of a straight line y=mx+b is m (the slope of the line).

[photografr7]

it's hard to explain without drawing a picture, but here goes... a function is a straight or curved line. At every point on the line there's a slope of the function (the line) at that point. When you take the "first derivative" of the function, it allows you to determine the slope of the function at any point. Did that make any sense to you?

[LondonBornGal]

Oh, Awesome. I can't seem to get enough of numbers. (not the TV show)

[killmodell]

that was really well done, thanks.

[dashromance]

you should make more of these, sometimes i don't remember how to do calculus and other math related topics after being taught in class, and watching this really helps me out. please do many more! it helps a lot of students. including me.

[tenneral]

brilliant explanation. I am enjoying calculus for the first time, and understanding it too!!

[byan213]

Great job! Your detail in explanations is appreciated

[TheFallibleFiend]

Qui docet discet. Well done.

[photografr7]

When you take calc in college, you are taught (like here) what is and what is not a function. Then you learn to take the first derivative of funtion...

[photografr7]

writing with your left hand is distracting... even for a math lover

[spareid1991]

excelent video. great that you took the time to do this.

Question: Is y=SQR(x) a function, even when x [0,+inf). +ve numbers have two roots (both +ve and -ve). eg. Sqr(9)= + or -3. The range is therefore larger than the domain. Or am I being thick?

[spareid1991]

should have been a ? after [0,inf)

[applexy]

Excellent Work! A great introduction to calculus. Please indeed create more of these great lectures :)

[Packersfan303]

thank you. im a sophmroe trying to teach myself calc and this helped a lot. ur a good teacher

[HookMe10]

good work, keep em coming

[homer30]

this vid made me feel so dumb

[fc007]

don't worrie, I think he messed up somewhere explaining what a function is.

[kisses4me124]

hgsa hjapd havvuu wittho no drey

[komet1979]

I have to take Calc III next semester.....drag:(

[websuspect]

Calculus is bullshit you can find all the variables using non constants in Algebra or linear Algebra.

[Alectr0n]

Cant you just solve "box size variables" algebraically?

I suppose that would become impractical with more complex calculations though. I'm just getting into higher math now so I'm a n00b.

[smartissexy]

Sure, algebra will allow you to find the size of boxes at moments in time. But suppose a box is growing, and we want to know how fast. Need calculus. Or suppose we have a limited supply of cardboard, and want to make the box with the biggest volume. Need calculus.

[sweetreview]

please make more demo videos!

[PilpLan]

great stuff more videos please

[flightlevel69]

not only are you cute as hell but you have an incredibly sexxy voice, too!! :-)

[uberkuh]

On behalf of all former art students, thanks for posting!

[KinG4L]

Great Video it's interesting keep making more videos!

[yayagirl88]

yuck =P i have a calculus exam 2moro and i watched this video..dude i still dont get it!!..but thanks anyways ;)

[dutchfucker]

hey sexy, are you a math ed major? or grad :p

[yangpu6]

A great Video. Thanks a lot! Seriously, thanks! Lovely.

[hek0990]

weird, at uni when you need to put in the effort, you end up cramming like crazy before your exams. but after graduation, you log onto youtube and watch out of your own freewill despite having close to no free time on your hands. and what's more, you think to yourself, "this crap i learnt was kind of interesting"...

anyway nice intro into first-year calculus, it brought back so many fond memories of me falling asleep in the lecture theatre...

[dpastor3]

dude that is so true!!!!!!!!!!!!!!!!!!!!!!!!!!­!!!!!!!

[Russoft]

In electrical engineering, we denote imaginary numbers using j instead of i. A complex number would be: 8.49 + j8.49, which can be represented as a vector, which we call a phasor, represented as: 12<45°

That is my only interesting input to this video.