Calculus I - Lecture 1 - A Review of Pre-Calculus

[mjm8030]

not for people that are advanced usually in a introductory class one would hope the student know what a function is and the notation but because he did not make a video on that he starts where many begin for me elementary school he probably had a fear that not everybody could follow him this is YouTube not a collage i like it because what he doing is reading a text to you slow and simply the ideas hope he proves stuff in later lectures  its a good model if you are trying to teach everybody.

[Zkylz]

30:19 .... he doesn't need the apostrophe. good thing he's teaching math ;D

[Moiez101]

FUCKIN HELL. THIS GUY IS BRILLIANT! I'm a philosophy student and i was getting this shit!

[freakygeniusful]

I'm in algebra 1 right now and we've already covered this....

[Mark6770]

But +-sqrt(1-x^2) is not a function right? is it ok use it in a step function in second discussion?

[Mark6770]

Very understandable!... its so clear to me...

[NajCarnage]

i'm currently studying pre-calculus, and i've learnt more in 5 minutes of recap than in 4 weeks of lectures. Thank you!

[fordsonhigh23]

OPEN MINDED TEACHER

[haydeeargentinar]

I am sooooooooo thankful of your video's you are amazing.. I WISH YOU WERE MY TEACHER.

[KamaniLankachandra]

Great Lecture. checkout my pathology lectures.

[ghostkingist]

good video i like it

[b4iFuRu15]

Wow. I'm 22 and I've always had problems in math. I powered through precalculus somehow after failing it the previous semester, and now I'm in calculus. This was so helpful. Thank u so much for creating/posting.

[rukus100821]

can you imagine that.... you can test out of the freshman courses with all the youtube videos that pertain too the freshman courses.

[jubyvera662]

booo it sucks...lol.

[Punkorealist]

6 people got an F in Calculus 1

[dekippiesip]

I have a question about the definition of a function. Strictly speaking you say a function is a rule that associates with each input exactly one output. But what about functions like f(x) = 1/x or f(x) = ln(x)? In the first the input x=0 is not defined and for the second there is no output for x=0 or x<0, they don't have an output for every input what contradicts the definition you gave. So are these relations strictly spoken not functions?

[gaplti]

@dekippiesip: It is true that to have a function, every input must have a unique output. A function can exist if certain inputs are excluded, though. In the case of f(x)= 1/x, this function exists except where x =0. Therefore, 0 is not in the domain (universe of inputs) of this function. Subject to that excusion, the range of outputs manifests unique results.

[peetyq314]

Great

[maxood007]

Excellent explanation of functions and detail related to them for beginners!

[flowewritharoma]

thanks for calculating this complicated calculation.

[Saronaist]

U r the best. God bless you.

[FellOnSoundGarden]

After 12 years of high school, 4 years of college, I can say with all sincerity Richard Delaware is the BEST math teach I have ever seen. I did fine in calculus in college, but never really had a firm grasp on it. Now that I am just trying to learn it for fun, it makes so much more sense. Thank you Professor Delaware, for letting me enjoy math. I cannot thank you enough. thank you thank you thank you

[TheLonghairraven]

can someone explain to me what is calculus??? a simple defintion??? I

[atreyu1210]

Does anybody know the name and degrees of this lecture-giving man?

[TheWinterShow111]

The other day I made a comment about a correction I thought needed to be made, but the comment was pretentious, incorrect, and I apologize sincerely both to the author of this video and to anyone who was offended by the stupid mistake I made. Specifically Shadowriku40 and Kendylkakes, It was unthinking, and I was all too quick to judge.

[afdwbspeedybri23]

I'm learnig most of this stuff right now and I'm a freshman in high school. But i did skip one math class, but this would be considered the basics of your 10th grade year. Great video though, helped me with my finals(:

[Kendylkakes]

@TheWinterShow111

You should really know your order of operations before you start talking a bunch of mess...

PEMDAS (Parentheses, Exponets, Multi., Division, Addition, Subtract) tells us that the first thing to do would be to square the -1. squaring a negative number gives you a positive. So, 3(-1)^2= 3. then -4(-1) makes a positive 4... so now it reads 3+4+2... Which is NINE.

Way to go...

[halo3ismlg]

@Kendylkakes stupid...listen to what he says...he simplifies the whole thing to nine...not just one part which youare assuming is that he's only trying to simplify 3(-1)^2...

[freakygeniusful]

@Kendylkakes

He wrote nine smart ass.

[Shadowriku40]

@TheWinterShow111 Dude, 3(-1)^2 = 3(1) = 3.

How about you learn your order of operations before getting into Calculus?

[abcdef1575]

Thanks a lot.This is Great for a quick review session. Youtube now works for the good of college students thanks to you good sir.

[akashashen]

Nice to see "The Mechanical Universe"'s derivative machine lives on in doodles. That's where I first got my mighty geek on in Jr High.

[FantasticLeo1]

thanxk

[blastburncannon]

thank you

[keithl28]

Thanks for the video

[ThedudeVip3r1990]

Thanks so mucho Teacher! god bless you.

[klebehss]

sure this is PRE-calculus ?? I did this in college algebra, the class befor pre-calculus .... in a community college

[alexatlanta1983]

Mr Richard you are the best teacher i have ever seen

[rysouza1]

240p? We meet again...

Oh hey Math, well I do have a Pre-Cal Exam in two weeks.

[abcdef1575]

@rysouza1 i have one in 2 hours.

[ToiletProjectIndia]

I don't know how to thank you, you have released thousands of students from prisons called schools and colleges.

[Shorty20122012]

at 12:38, you're describing the function f(x) = |x|, you say that if x is negative, the slope is -1, and if x is positive, the slope is 1.

Does this imply that if x is negative, then the slope is 1(-x) = -1, so that the slope would be included (but invisible) inside the absolute value sign like this:

|(1)(-x)|

Because otherwise, how can the slope become negative if the 1 is outside of the absolute value sign? Thanks.

[jelopez71]

This is most awesome! Thank you for producing such great material! 

[topdawg567]

I'm a senior in high school. I need a teacher like this next year in college. lol

[videomakerman1232]

Thanks my first calculus video.

[Moshikashitenai]

That circle isn't centered on the origin, silly :)

[esraretin]

11:27 is multiverse something like it?

[esraretin]

universal language

[MrHotcrossbuns]

had to turn off my tech n9ne to learn calculus

[Nicola72av]

What a beautiful lecture!

Professor Richard Delaware, thanks a lot for all your interesting and useful lectures!!!

I send you a dear greeting from Italy.

Nicola

[neversaynever234]

@arafiq29 Dude seriously? grow up i have friends who are dyslexic and i don't joke around making fun of them. wtf is wrong with you dickhead.

[ChibDibs]

@neversaynever234 lol. that's pretty hilarious.

[kiraofthewasteland]

this guy is a awesome writer O.O

[DyDxTutor]

Good Lecture on pre-calculus

[205231228]

i wish u were my teacher

[GrandMasterJuan]

can i download the vids ?

[WildMonkey42]

Currently in Pre-Calc. This man helped me understand in 8 minutes what my teacher could not in 2 days.

[Sorbik]

nice crash course in pre-cal.. which i'm taking now and know nothing about

[sajje17]

I found the lecture quite useful.The video got stuck at 34:22 minutes.Plz get it fixed.

[805PiGGy805]

46 minutes ?!?!?!?!? is that even possible ?!?!?

[virusmakers]

@805PiGGy805 for a smart person like me yea for you no

[anatete1]

@805PiGGy805 Yes, it's possible? Can't you see? There's evidence on the video above.

[ashishkrrai]

hello sir, Just wanted to tell you that your lectures are so gr8 n awesome......so can u plz post some tutorials on some other mathematics chapters too....

Greetings from India....:)

[thesqaanalyst]

Thank you professor.

[GDWS81]

You Sir, are a good man. Thank you.

[Tazmaniak89]

you are amazing. thank you so much for all of these videos you provide for us. Do you have a donation button anywhere? I'm a college student, so I wish I could give more. But you've helped me so much. more than any math teacher has been able to in person. I don't know else I can thank you.

[changeonslecongo]

the nobel price must be awarded also to men like you...even poor who cannot afford to study at Harvard or UMKC are able to get good lecture online..thank you very much

[frogca]

This what the power of the internet is all about. Professor Delaware is a god send. I actually love math now and I use to hate it.

[bangalorebully]

@frogca "Used to hate math and love math after Delaware"???Same here mate!!..I am near the end of his algebra series now...after that some Trigonometry and then this calculus series on the menu...How far have you gone??

[surferdance]

Thank you. I follow you so well, almost effortlessly. You are inspiring me to be a teacher!!!

[neverrime]

Why are you spamming the Youtube with your silly math talk? Don't make us go after your little ass.

[OUsooners209]

I'm learning this in the 5th grade, and I'm having trouble comprehending this subject.

Practice makes perfect...I'll see about that!!

[AEVautomatic]

he is telling lies don't listen to him its a trick!

[TKgeniusHELLTX]

I'm using these videos to get ahead of my couses. That way when I get into my class at my college I'll be balling :D A MUST FOR UNDERGRADS for a B.S EE!

[goonhilly1951]

So glad that I found your YouTube lectures and appreciate the effort that has clearly gone into these. I am a 60 year old surveyor in the UK and had this yearning to re-learn calc after messing up my advanced maths in high school in 1967. Partly due to the awful standard of teaching. The guy that taught me never bothered with you unless you were a brain box and use to assume so much and swept past basic intro stuff and have spent a few hours tracking your stuff.

Regards goonhilly1951

[monikawashere]

@goonhilly1951 i dont care if this story true or not, but it is really boring

[XxBaRHoMxX]

thank you so much

you helped me a lot

[frostwow]

this guy is my second father

[SlashSkull]

i love how you have this creative idea of using the powerpoint project as your green screen replacement background

[ryandrums1001]

woot woot you're the greatest teacher and explain it so well, I'm on my way to learning calculus at the age of 15!

[AVeLLiiii]

Why is that @ 16:06 when he says if x is grater than or equal to 1 he automatically places a (Y) value of 1 on the graph with the 1<or = x?

[VVillowz]

Prof. R.Delaware at 11:00 you explain the vertical line test. Can you tell me why is it an IFF statement? What does that mean that it is an IFF statement? How do you know that fact? Thank you.

[pableras96101]

no lo entiendo

[comptonhicham]

thank uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu­uuuuuuuuuuuuuuuuuuuuuuuuuuuu From Morocco

[Antiunfunktasticize]

So, I don't really have the patient to watch all of this, but I did see the first 5 minutes then skipped around to get as much as I could. I have a question though, is precalculus just Algebra 2? So far I've done most of this in Algebra 2.

[darkomen46]

@Antiunfunktasticize Precal covers topics in Algebra and Trig.

[xxthunderbird46xx]

You Are a math god! Thank you so much for making such a helpful review tutorial :)

[Kininet]

Thank you so much. You are great.

[MrMohamedmohamud]

i regret, i did not get these videos early! even personal tutor can not make me understand like that... you could pause the video and figure out, also you can repeat and repeat any time. thank you thank you thank you again and agian

[Goldname1]

today my mom suddenly burst through the door, smacked me across the face and said "YOU HAVE 4 MINIUTES TO LEARN CALCULUS!!!" I replied "..." So here I am.

[SHAMMARYS]

Thank you very much Professor Delaware, I appreciate you for this lecture

[psycosquirrel789]

This is great! Thank you so much for sharing!

[iwillbd1234]

Thank you very very much. I'm only a junior in high school but I'm using this to get ahead of the "game." Hopefully to graduate early. So thank you :)

[bobflipinHHH]

YOUR AWESOME, i am really understanding this thank you, i will be taking pre-calc soon and this helppsss alott!!

[purpleleach1]

Why would it be a circle if both the (a,b) & (c,d) are the same and the circle looks like an ellipse? But when (a,b) & (c,d) are different and it looks like it's a circle, it's a circle? if the radius is 5 in both directions.... it should looke like a circle...., maybe I'm wrong, and according to him I am wrong, so can someone plz explain this to me? thankyou

[mtaddess]

Thank you so much. I haven't taken Calc I in 5 yrs & I am currently retaking it, so that I may move on to Calc II. I work fulltime, attend school fulltime, and I am a single mother. It is for those reasons that I do not have much time to remain on campus to get extra help. Your videos explain everything in an easy to understand way and help me to understand the questions that I wish I could have the time to ask my professor in person. Thank you! Thank you! Thank you!!! I cannot say it enough!

[IdleWild999]

Not sure your definition of a function as 'each input producing a unique output' is entirely accurate, a good example to the contrary being x mod 2.

[mathbards]

@IdleWild999 This definition of a function is entirely correct. x mod 2 is not a function. Nor is x^2 + y^2 = r^2. A function may only have one output per input value. The converse, however, needn't hold. That is, for every output there need not be a unique input. A simple example is y=x^2. We can see that for every x, there is exactly one y. For every y, however, there are exactly two x values. eg y=4 means x=2 or -2. y=9 means x = 3 or -3.

Hope that helps :-)

[mathbards]

@IdleWild999 

[mathbards]

@IdleWild999

That is exactly the definition of a function.

[redcardsoccer]

my brain scrambled

[yuriynyr]

Excellent. I will be taking Pre-Calculus in the Fall and this has been a great introduction which will no doubt make it easier later on. Thank you.

[Aznhick]

Thank you so much for sharing these videos so that everyone can learn from them, not everyone can learn from any teacher and having the most available is just the best thing.

[MrLumierre]

thanks professor,

your videos really help

kurt

-2nd yr university of the philippines

[9343105697]

thanks

[9343105697]

thanks

[Tamlin2308]

I love this guy. Please pay him more.

[leparditas]

how this video is made. i mean rhat you can see two views in on screen...

[dentalplanrage]

@leparditas I would imagine his face is recorded in front of a green screen and the video of the paper is recorded on another camera, then put in the background during editing.

[punkskarocker22]

Dear Prof. R.Delaware,

Thanks so much for uploading.

This supplements my nightly sleeping.

Not only is the video well done, but I can just listen to the audio, and immediately fall asleep.

Thank you so much!

Thank you very much

[yesilful]

You are much MORE miles better than mit calculus lectures. Will you upload advanced calculus lectıres and also some point set toplogy.

[ammsa7]

how do you restrict a domain of a function to a specific range?

[kingbersalona]

I KNOW THIS SOUNDS CHEESY but People like you and other great educators who post videos like these on youtube should be given an AWARD or something.

If only you know how helpful you are to the WHOLE WORLD.

Just let us know how we, as free users, can donate to / help your school produce more of these videos. THANKS (raised to the 10th)

[chulababy20]

why cant all teachers be this good? thank you, i wish i would have found this earlier.

[athor04]

thank you thank you thank you :)

[El3ctricPenguin]

A 45 degree V? Nice try, that's a right angle. (12:27)

[MsMitson]

thanks professor :)

[gurmu1]

thank you!

[docubloke]

This is excellent. Very clear explanation of the subject matter with plenty of helpful illustrations. Well done!

[macaroni610]

maybe i wont drop calc after all.

[Schutzstafell]

I thought Calculus was mandatory.

[sattam5149]

Thanks professor , you're method is really helpful.

[ThunderAppeal]

I've been trying to buckle down and read some math books but the subject matter is sometimes very dry for someone reading it on their own. I stumbled upon your Algebra videos and it is all starting to come together and make sense to me. Professor Delaware you have a talent for breaking the subject of mathematics down so that anyone who is willing to learn can learn it. It is videos like yours why sites like youtube exist. Your videos have inspired to me work out math problems on paper onmyown

[saleh371]

Thank you Professor Delaware. it is really hleped me alot.

[payamem]

Dear Professor Delaware, I would like to thank you very much for your great intention of helping students with calculus and Algebra .

May almighty god bless you and your family. Would you please let the students know if there would be calculus 2 lectures coming up as well or is there any way that I could obtain video lectures of Calculus 2.

[poolie626]

@payamem as well as 3 please

[catch33rampride]

great video, can you do tensor calculus or abstract series? it'll be SO VERY helpful! thanks!

[hensoning]

thanks for the lecture, calculus is one of the subject makes difficulties for me,

thank you sir for the tutorial,, im henson from philippines

[sismancocuk]

Professor,

I truly thank you very much for all your effort to teach Mathematics in such a way. Some people prefer to make it hard to grasp so the others would think that "this guy is smart. he understands Math!"

I still see professors who are not really able to teach but show how smart they are. I think we should remember what professor Skiena has said couple of years ago: "That crummy professor couldn't teach their subject, but they sure taught you how to teach yourself!"

Thank you very much.

[zagros24]

thank you, thank you, thank you Dr. you're a great teacher.

[xxibe]

Thanks for putting up your videos. These are quite helpful for me especially since I am a foreign non-traditional student.

[thecollegesagateam]

Dear Prof. R.Delaware

i'm a boy from boston in the 7th Grade watching your vids and they a really useful

i really understand everything that you are saying thaks for the lecture

- thecollegesagateam

[indiaman1970]

Dear Prof. R.Delaware,

Thanks for these wonderful lectures.You are an exceptional teacher.

The greatness in your teaching is due to two facts:

1.You explain even the simplest of things without assuming the student already knows it.That's refreshing.

2.You explain all your examples with graphs which makes it so easy to understand.

I can't thank you enough for these excellent lectures.

From a grateful INDIA .

P.S. Lecture 18 II missing,Lecture 28 incomplete,Lecture on Volume I not there.

[UMKC]

Hi Indiaman,

Lecture 18 Parts 1 & 2 were combined. Not sure which lecture you are referring to when you say Lecture on Volume 1 not there.

Appreciate the feedback and glad these videos are useful

UMKC admin