ALL OF Calculus 1 in a nutshell.
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- Опубліковано 31 лип 2024
- In this math video, I give an overview of all the topics in Calculus 1. It's certainly not meant to be learned in a 5 minute video, but this should give you an idea of what calculus essentially is at its most basic level. I worked especially hard on this one so I hope you guys enjoy!
0:00 Introduction
0:06 Functions
0:55 Limits
1:36 Continuity
2:27 Derivatives
3:09 Differentiation Rules
3:35 Derivatives Applications
3:57 Integration
4:38 Types of Integrals
My focus is to help people who don't necessarily like Math finally appreciate its beauty. I want them to see that Math isn't all too difficult, and once understood, Math could be really cool : - )
After passing the class with a C, I can confidently say that Calc was deriving my brain crazy, I am at my functing limit. But even though my hatred for this clASS is Undefined (especially at the origin 💀), I really liked your video.
A perfect remainder for integration topic : Always add + C
@@SuryaBudimansyahI got a 99 of 100 on my calc 2 midterm because I added a plus C to a derivative question 😔
bro thats so good btw dont be such a nerd @@noodle7788
@@noodle7788 skill issue
Neat
This is the perfect clip for the 1st class in calculus. Then, you should ask students how they think about it, clarify it for the next 45 min and then, start the traditional course for real.
Straight to the point and not padding for extra watch time? You earned my subscription!
nobody needs to earn ur subscription ☠ who are you bro
@@respectable2540 cant be talking all that when you shit at fortnite lil bro
@@respectable2540 dayum chill bro
why did you feel the need to share that information
bro wrote a yelp review on youtube
Amazing Quality of Content
- Simple and Easy to Understand
- Short and To the Point
math exam in 5 minutes wish me luck guys 🙏
I think this is amazingly done. Its very concise and gives a simple and elementary overview!
Seems so easy looking back compared to the amount of differential quations I have to do now
I think this is the best video I have ever seen about basics of calculus and what it is
Perfection!
this video is SO GOOD. i was completely forgot all of calc 1 and was feeling overwhelmed trying to review my notes. this broke everything down so clearly
I love this video so much, super explicative with great visuals
Wow!! really cool video for many students new to the subject.
That was pretty dope ^^
Good summary. The execution of it is much harder tho hahaha
The concepts seem nice, but my fear of resolving them is bigger.
Idk why but in class i can be focused and paying attention but have no clue what im actually doing, thank you for giving labels. Its always hardest to know where you are struggling when you dont even know what its called to ask for help. differentiation rules, yes! I have a name! thank you!
I watched this video at the beginning of the semester and it was all gibberish. What a wonderful feeling to rewatch it at the end of the semester and actually know what all this means!
Since you just finished calc 1, might I suggest watching my calc 2 and 3 videos 👀haha kidding aside, glad to see it (seemed like?) you enjoyed your calc 1 module!
This shit's awesome man, keep it up and you're gonna succeed
Appreciate it!
It's nice to finally watch this and understand everything.
Im currently taking AP Calculus AB my senior high school year and we’re currently on derivatives 😁
So far it hasn’t been too bad
i’m in the same position! i have a test on limits soon lol
I’m loving my ab class so far. Easily my second favorite class being physics c m
I just started AP Calculus BC my senior year but I never took AB, honestly all of the AB stuff was super easy to understand just dont second guess yourself and you'll do amazing!
@@nyro5403 yea. I’m self studying for bc since ab concepts are pretty easily. Like I learned basic derivative and integral stuff in like 5 minutes, so imma just do bc
Very helpful, thank you, the intuitive explanation of calculus.
I wish you'd been my Calculus 1 teacher. I would have actually learned it.
Thank you for this! I really had such a hard time understanding this
I love it, this helped so much
I’m a sophomore, just started pre-calc so I’ve got a little while before I get to this obviously but these concepts don’t seem overwhelming, like yeah I don’t understand them now but I feel like I’ll be able to handle them
As a junior who is studying calculus, I can confidently say that you're completely right. You might not get everything now, but you will when it's time to do so.
I just learned all the derivative rules and I was wondering what was next. I knew the gist of it, but not what exactly we would be finding. Thanks!
You have a long and fun journey ahead! You can check out my calculus 2 video to get a preview 👀
You did a really good job so congrats. 👍However, you may want to focus on other areas of math as there are already thousands of way superior videos on this exact topic.
Thank you so much for the video, it looks like an amazing primer for calc and is something thst I have no doubt will help allot of students out when it comes down to to application of calc
Thanks man, subscribed
Best 5 minutes and 23 seconds of my life
Im taking my first calc class in uni this fall.
You just saved my butt!!! Thx
MATH IS SO COOL
No.
@@arneshpal7702 Yes.
@@arneshpal7702 Yes.
Wait till Riemman's Tensor comes
It is until you get to highschool and the information is taught in the most esoteric way imaginable
Looking back at calculus after analysis lol simpler times 💀
ah yes the point where u realize school was going easy on u lol
thank you!
This need more views
TRULY A BEAUTIFUL WORLD 😍
Integration and the fundamental theorem of calculus probably deserve a separate video.
I don’t think “area under a curve” quite hits the mark when it comes to describing the integral. For example, I was recently pondering how I might calculate how far the tide would come in at high tide if all I had was a function of shore angle with respect to height. There are probably better ways to do this, and I might have been wrong, but my speculative answer was to integrate the angle function from h1 to h2, take the cotangent of the result, and multiply by delta h. The only condition is that the angle must always be greater than 0.
Ok
That face when calc develops "time travel" via "divergence" makes just as much sense as "imaginary numbers"
TBH there is limits, then there is derivatives in a way that makes you format them in a way where you will get it wrong if you oversimplify it, then next there is the easy rules that allow you to correctly simplify the derivatives rather than ending up with a weird half divided thing
Cool I’m just going to test out of Calc one after watching this
hey do calculus 2,34 i loved the style :000000
crazy how its been less than 1 month and my calc bc class is already done with derivatives
really fucking nice, but i was left questioning how to use a derivative in an applicated example (i mean, the explication on how to use derivatives in the examples you gave)
still, i love your videos man ❤
Appreciate it! Atleast for the physics example, the derivative of the displacement time function gives you the velocity time function. Similarly, the derivative of the velocity function gives the acceleration function. Personally though, I find the optimization example much cooler, but I'll leave the fun of discovering that on your own
Every engineering problem is collection of differential equations. Mass action law, ohm's law, fluid dynamics, compound interest,
@@arolimarcellinus8541even in biology and life sciences. the growth of a population, amount of medicine in a person over time, virus infection growth rate
I SEE AND I LEARN.
I did some of this in AP calc Ab. Does this class use calc 1 stuff?
Passes Calc 1 with a B but failed the Credit transfer just to be put back in Pre-calc and set to retake calc again in the summer. Love School.
I saw the pepe and immediately autocorrected all of calculus to ALL OF CIRCUS.
Damn this is accurate!
I can dig the formulas and the need for simplifying equations. I just cant wrap my head around the concept of infinity......
A Trip To Infinity, I think its on Netflix, but specifically the infinite hotel part really helped wrap my head around the concept of infinity. Its awesome and I highly recommend it.
@@ToastedRen Thanks, Ren!
this man does in 5 minutes schools do in 5 months
Wow wait that's actually it. I took honors calc last year and this year im doing ap and that about sums it up
thanks youtube's for recommend me this video
nice video, even though I don't understand most of it. I'll comment back when I've took precalc honors
took hon precalc over the summer. its a breeze, you can do it
i wanna take an engineering career in college, but i've always hated math
but after watching this, calculus 1 really doesn't seem as complicated as i originally thought it was 🤔
As someone currently taking Calc I, it's mainly just people explaining very simple concepts in very confusing terms. Learn to translate math notation into plain English (like this dude did in the video) and you will excel. This also separates great math teachers from terrible ones IMO
@@plaguepandemic5651 This is so true. Its hard to follow along with calc teachers because they treat math notation like the symbols are intuitively translated to english.
Calculus is just Algebra 2 with a few new symbols that are just there to scare you
that's a better way to put it lulz
i'll keep that in mind
WOAAHHHH
how did you make this video? Which software you used ?
Yup. That's about it.
Implicit functions break straight line test
❤❤
yes
Do one for Calc 2 and 3
just uploaded the calc 2 one!
It’s funny that we’re already on continuity in my first week
Man those are called piecewise continuous function
I’m in AP Precalc, so hopefully we will cover everything in this video at least briefly
Wait wtf there’s an AP PreCalculus now??
@@karthiktirumala1773 yeah lol it was introduced in his year
@@evangibson149 isnt it just pre-ap cal though?
you wont lol, ap precalc is just alg 2 with some more stuff.
@@evangibson149 idk about AP but when I was in high school, I learnt about Limits and basic Derivatives in PreAP Precal
I think im weird that calculus was my best subject in highschool (even higher than ECONOMICS which is middle school algebra) and 12th grade here is as hard as university level
👏👏👏👏👏👏👏👏👏👏
i watched it at 16x speed i think im a mathematician now 💀
Damn i wish I could watch things in 16x
@@evangibson149 if ur on laptop, i add this js code to make it faster:
javascript:document.querySelector('video').playbackRate = 16.0;
yea now be a mathematician 💀
🎉💕
what about series and successions
I usually see series, most commonly taylor series in calc 2. I'll be making a vid on that soon!
Question!! so basically, if we're asked to find the derivative of a given function, does that mean that the given function is already the area under the curve considering that the opposite of derivation is integration?
Yes! However, be careful with constants, as technically integration yields infinitely many functions (the reason for the "+C").
For example, the integral of f'(x) with respect to x is f(x) + C, and by evaluating it at two points a and b you get the signed area of f'(x) BETWEEN a and b: f(b) + C - (f(a) + C) = f(b) - f(a). Notice how the constant disappears.
However, evaluating at only one point only gives you the signed area if you happen to get lucky since we still have the annoying constant term: f(b) + C
The FTC II summarizes what I've just said in a neat formula.
To add to R3birth's answer, it's also important to note that "area under" is not necessarily interchangeable with the "anti-derivative" because integration does not guarantee differentability of F _and_ equality of F' and f. In other words, you're safe going in the direction that you're talking about: when you know F is differentiable on an interval and F'=f, then yes, F is the both area under _and_ the antiderivative of f=F', but you can't assume differentiability or equality going in the other direction, even if the indefinite integral accurately describes the area under f on a given interval.
For example, take f:=sgn(x), right? The function f is integrible on [-1,1] and you get the indefinite integral F:=|x|-1, but because F'(0) doesn't exist, F is not the antiderivative of f with basepoint -1.
Thomae's function (aka the modified/reduced Dirichlet function) as h(x) is another classic example of this where H=0 because countably discontinuous* points do not have an effect on integration. Obviously H' exists and H'=0, but because h is Thomae's function, H' doesn't equal h when x is rational.
Probably not super important to keep in mind if you're just doing worksheets or whatever, but it's a good corollary of the Second Fundamental Theorem to point out. Basically, the antiderivative F must not only be differentiable on _all_ points on the given interval (the sgn(x) example), but F' must _equal_ f at all those differentiable points in that interval (Thomae's function example).
Also probably worded some of that poorly, but the tl;dr is that the first part of your question is correct, as R3birth explained, but the "opposite of derivation is integration" part is not _necessarily_ correct. The opposite of the derivative is the antiderivative, and the indefinite integral may be the antiderivative, but it also may not be because the definition of antiderivative is more strict than simply a function being Reimann (or even, more generally, Lebesgue) integrible!
*Edit: it is probably worth expanding on what I mean by "countably discontinuous" here, if you haven't heard the term. Thomae's function is "countably discontinuous" because h = {1/b when x=a/b is rational, and 0 when x is irrational}. Because any rational approximation of an irrational will have a very large denominator b, we can say that for any irrational x, there exists a sequence of rationals (xn) where each rational xn is a better approximation of the irrational x than xn-1, and for any ε>0, there exists an M s.t. for all n>M, |h(xn)|
This accent sounds Filipino. Are u Filipino?
Edit: also great vid man, the way my school explains calculus is terrible
hahaha i love how the first thing i noticed was the accent and was abt to ask the same thing
Yes I am
Thanks bro.
Got 2/30 in this exam. Then I switched to Political Science and everything's going well
POLITICAL SCIENCE MAJOR
@@sheepcommander_ LOL
I'm sorry you failed calc 1 bro ✊😔
Like 90% of my former classmates😂😂
Great video. I hope Isaac is looking up from Hell and proud of his legacy
when they didnt cover the 3d application of integration with inverse square functions, thats when its no more fun and games
Not going to lie math is much easier than I remembered
wow math
Waiting for the calculus 2 video.
ill upload soon! swamped by other responsibilities right now 😅
Am I the only one who can't recognize a thing (except for the axis one )in this video? I'm about to start may college life in BSCP course and I don't understand a thing
MAFTH
You lost me at limits
You sound like Matthew from the chosen
wait theres a sequel?
soon!
Quite a few mistakes in this video, but it was especially sad that you didn't include the Power Rule for derivatives
You forgot squeeze theorem.
QUÉ FACIL CARAJO
Ok so what you're saying is our Pre and Basic calculus in junior high is just the begging? Man im so done
did you forget the power rule
now do calc 2 PLSPSLLSPLPSLS
Thats when math was easy😢
"So easy"
* epsilon-delta proofs and Taylor series appear *
Expected a joke video w/ memeing on cal 1 ngl w/ that pfp and thumbnail
me no understando
Not Limit definition, not real U calculus, well, maybe for engineers I guess
Well, you didn’t include disk/washer method, and cylinder shell method. But I’m assuming most calc 1 professors don’t teach it until calc 2
Disk washer isn't some fundamental method for anything
Just specific application, u won't use it ever again after that, and really it s just basic integration
Watching this at 2x speed
So its basically high-school calculus
yeah im killing myself
All of this is high school math in greece. Why would they do this?
This is highschool math in the US as well, so you might be thinking of college calculus 1, a class with the same name but much harder content, usually taken in college or university.
I got nostalgia, now I’m in calculus 4 class
Wow. That was way easier than calc I, and yet so much less rewarding.