Hi, welcome to the third week of the Calculus course.
Recently, we have covered
concepts of limits for various entities.
Sequences, single variate, and multivariate functions.
Now, it's time to turn to
more sophisticated and far
more famous subject; derivatives.
It's just a common knowledge is
that Calculus course is mostly about derivative.
The problem here is that
most people didn't realize that it's not very tense.
So anyhow the proper way to properly start
to study something is to
understand to why we're studying it.
So imagine the following case.
Assuming that I have to travel from home to
work, say 100 kilometers.
Well, say it takes two hours for all the way.
As such, my average speed is 100 divided by 2,
50 kilometers per hour.
Say the limit here is 80 kilometers per hour.
It doesn't necessarily, mean
that I will not get a ticket for speeding.
Well, in case I was driving all the way versus
same speeds which is
my average speed or I'll exit blue curve on our graph.
It's actually right.
But in a real life it's not,
in real life my 50 kilometers per hour
arguments won't stand in court because as the court
actually cares about whether
I was driving under the limit
all the way through at every point
of my way and every point of time.
So in order to
understand whether or not I am getting a ticket,
we need to introduce ourselves
to concepts of instantaneous speed,
the speed of change of
my distance from home at every moment of time,
and that's what's derivative mean.
So in the following week,
we are going to firstly define a derivative,
understand basic arithmetic rules for it,
and then move forward
linear approximations with the use of
derivative and derivatives of higher order.
So let's begin.
I'll see you in the next, in the following video.