Basics of Calculus (1 of 5: Foundational language & notation)

[VictorOrdu]

Teaching is indeed a special art reserved for a privileged few. I've never seen calculus explained this way. Thank you, Mr Woo!

[grahamkerr]

There's a subtle, but powerful, art to teaching; and teaching well. Individuals don't fully appreciate the impact a great teacher has on a class. Any class. Whether it's maths, science, politics or whatever, if you're being taught by someone that exudes the same level of enthusiasm he or she wishes to impart on everyone else, then that's an absolute game-changer.

[Roshambo]

Wonderful teaching. Love the way you tie all concepts together and help paint an understanding of the WHY behind all of it. Thank you!

[asmd]

Mr. Woo, thanks for the video. Helped and inspired me a lot!

[tanushka]

Conviction/beliefs - the world needs educators, though, I can’t accuse/humiliate someone for their disabilities, people should work on! I need to thank you, 'coz you’re one of those educators who believe in diligence!

[songshenzhang]

Awesome video! I immediately got an A for my test after listening to Eddie Woo Sensei's teachings.

[piggo]

Watched some other videos about calculus by you and had no idea what the words meant. This is so clear and I understand it so easily!

[mariedillon]

Thanks so much for your exceptional teaching in these videos. You've really helped me as I'm learning maths on my own☘️😊

[nplgwnm]

If Eddie was around a decade ago, I would have got an A in my Calculus class LOL

[lourinsabrenica]

Thanks Mr. Woo.
This helps me a lot in my college subjects

[MichelleJudy-sn]

Man! This lad is

He makes me fall in love with calculus...❤

[Ztingjammer]

A very nice and clear introduction into Calculus.
Am loving this ❤

[monoman]

england supports your good work..thanks eddie..

[Mojud_Zikr]

Again thanks for this videos.... Calculus is some kind of difficult part of my maths knowledge but, I know u videos will help me a lot.... Love from India 😍😍😍

[VIC]

Thank you teacher.

I think that I understand it all!😮

We have a curve.

We have a straight line crossing at two points.
It's called a secant.

Each point has its coordinates.
Eg. [x1, y1], [x2, y2].

The gradient can be found by the quotient of the difference of their coordinates.
Eg. [ y2-y1/ x2-x1 ] or [ dy/dx ] or [ ∆y/∆x ] or [ y2-y1/h] where 'h'= x2-x1 or ∆x.

If the curve is described by a function 'f', the gradient of the secant be described as f(x).

What if that secant is displaced so that it touches the curve at one point? That is, the line is now a tangent to the curve.

We can find the gradient of the tangent at that point by deriving a gradient of a tangent function f' from the gradient of a secant function f.

To do so, first we will limit the change in x to be approaching 0.
Eg. [ lim ∆x -> 0] or [ lim h -> 0 ].

Next we would use the function f' (x) which is the function that outputs the gradient of a tangent.

DIFFERENTIATION is the process used for deriving gradient of tangent function f'(x) from a gradient of a secant function f(x).

The output function f'(x) is called the DERIVATIVE.


Question.
What is the input 'x' the functions f(x) and its derivative f' (x)?

[ellyharvey]

How privileged these students are to be taught Mathematics by Eddie Woo!

[divyaraghavan]

Thanks Eddie... The video gave me more knowledge about calculus.

[AugustinSteven]

This a comment about maths terminology differences between countries. His Rise over Run reminded me that he normally says On for divide as in 3 on 7 for 3/7. I'm from England and I always use Over as in 3 over 7 for 3/7. He should really say Rise on Run to be consistency.

[沈博智-xy]

both pronunciations of secant are accepted I suppose. I think one's more dominant than the other though. Just like how there are two ways to pronounce laboratory.

[joshuatamer]

Sir could you explain why the integral of e^sin(x) is non elementary?