Calculus 1 Overview, (the connection between limit, derivative & integral)

What is calculus? Let me give you a brief overview here and a quick run through. Hopefully, this isn't just a class that you have to take in order to transfer.. : )

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[TheLethalDomain]

For anyone studying Calc 1, just remember that in terms of Algebra, Calc 1 is like learning addition and subtraction compared to what's available in the field.

After this, you go into multivariate calculus as you slide between Calc 2 and Calc 3. By that point you learn the equivalent of dividing and multiplying on the scale of relative complexity.

But as well all know, the point of algebra is to get us to solving equations using algebra. Well, the same will end up true with calculus for many of you going further into math.

The equations that require calculus to solve are called differential and integral equations. I consider Diff. Eqs. to be a sort of "Calc 4."

But let's say you want to imagine adding two more classes of Calculus that will allow you to more or less master the concepts internally.

This is when you actually learn the true underlying reality of calculus. This study is separated into many, many fields, all of which are summarized as "Analysis."

Let's say there is a Calc 5 and 6. This would be Real Analysis (study of change of real numbers) and Complex Analysis (study of change of complex numbers). With this, we can say that calculus is both the real and imagined analysis of change.

However, beyond this exists all the subfields of calculus that are specialized towards whatever you wish to accomplish involving systems that change.

[bigchungus]

My teachers, (who I love by the way) were never able to teach me this stuff, now I'm up where I should be, so that I can get into engineering collage. Thank you.

[holyshit]

6:30
For area and circumference of circle we can use idea of Archimedes
with inscribed and circumscribed polygons
In each step we double number of sides and halve the angle
We will get two sequences in that way and we need to calculate the limit
Slope of tangent line ?
What we will get if we calculate limit
(limit of "Algebra slope")
Area under curve ?
Lets divide it to pieces that we know how to calculate area, sum these areas and take the limit

[Ironmonk]

Great intro video to Calculus 1. Teachers needs to seat the point on the 1st day.

[steliostoulis]

Can't wait until Calculus II #yay

[hxunefunjqmozebk]

I used to watch your videos, which helped me so much last year, but recently I had a lot of exams and didn't have time for anything. Right now I'm facing another kind of difficult problem, couldn't find anything to solve it. The problem sounds like this: Find "a" a real number, so that integral from (-a) to (a), of (x^4)/(e^x +1) is equal to (-32)/5. It's enough if someone could give me at least some tips. Thank you very much!

[krishnannarayanan]

Very helpful for young me, now I can watch your calculus videos with some understanding!

[anthonytam]

getting a head start on calculus here! #yay

[bamdadtorabi]

#yay If you can give an overview of Calc II I think a lot of us would appreciate it. Thanks for every video you've made!

[rvzndsy]

I follow you bro i love math and physics i am from Egypt 🇪🇬, math help me in life

[joso]

Could you show us the demonstration that π is irrational?

[Salehalanazi-]

i respect you so much, hard working and you make great videos, can you please explain an easy way to graph tan or csc sec cot i found the normal methods doesn't explain it well

[betatester]

Care to add captions for the hearing impaired? and those who can't understand your accent?

[wellbangok]

I wish you could have uploaded this 2 years ago. Would have saved me a lot of tuition lmao.

[franchello]

We didn't cover integration until calc 2. But that was over 15 years ago.

[gytisvejelis]

can you make series explaning everything in more detail?

[stephenbeck]

Good intro video. You should end your Calc 1 course with the old “calculus in 20 minutes” video for a wild recap.

[obinnanwakwue]

Proving area and volume is great. #YAY

[Koisheep]

Am I the only one who read "study of changes" and heard Vi Hart singing "It's calculus! (Looking at slopes)"

[nickthorpe]

I really wanna see your Calc II overview!!