If you are watching this, then you must finally be ready to learn Calculus.
First of all, Excellent work! It's not easy to learn all of the required Algebra and Trigonometry
just to make it this far. Unfortunately what lies ahead is no easy task
either. So before we get down to business let me give you an overview of what to expect.
You can decided for yourself if you are ready, and when you are, I'm here to help.
So what is Calculus? When it comes to calculus you'll find that
it's very different from much of the math you've probably studied so far.
This is because calculus is the mathematics that deals with change. What's that supposed
to mean? Let's take a look at a simple example. Let's suppose we have a car that goes exactly
25 kilometers per hour. I If it drives for 3 hours, then we can find
that it will travel a total distance of 75 kilometers.
See, nice and easy, but this is not the change we are looking for.
Now let's suppose that due to road conditions, or the drive the car is speeding up and slow
down. In other words its speed is changing. Now
that we have a more realistic problem, how can we determine how far the car will travel
in 3 hours. The answer lies in calculus, and it's just
one example where we want to be able to mathematically handle a change.
Here is another quick example. If I want to model the volume of a balloon,
you might assume that it's approximately a sphere, and then use the formula of V = 4/3
pi times the radius cubed. This shows that the volume of the balloon
is related to the radius. Now when I start to let air out, things start
to change. The volume is decreasing, and so is the radius.
But how are these changing quantities related to one another now? What is the formula for
this change? Again, the answer lies with calculus.
So in order to tackle the problem of changing quantities calculus picks up three powerful
tools. These tools are: limits, derivatives, and
integrals. Now there are many other things you'll learn in calculus, but these 3 things
are the most essential. Because of this you'll want to spend as
much time with them as possible. Limits are the tools we use for precisely
describing how a function approaches a value. Derivatives are the tools we use for describing
how a function changes, and integrals give us the area underneith
the curve of a function. Using limits, derivatives and integrals calculus
can solve a variety of problems like where sit in a theater for optimal viewing, or even
how to make the perfect soup can. One of the most fascinating aspects of calculus
is how all of these tools are actually related to one another.
Even though they may seem completely different, derivatives are built from limits, and an
integrals can be viewed as the inverse of a derivative.
Of course you'll learn all of this when we start to dig deeper into the subject.
For now, know that calculus can be difficult, with many new ideas, terms and procedures,
but we learn it because it provides a better way to describe the world around us, especially
when it comes to change. Hopefully that gives you a better idea of
what Calculus involves. If you are ready to learn more then check
out the rest of my calculus videos. Thanks for watching.
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to my channel! If you want to see some example problems from
calculus, you can find those here. You can also skip ahead to the next lecture
where I cover the average rate of change of a function.
Of course I have many more videos that can be found on my website: MySecretMathTutor.com
So don't forget to stop by. Thanks for watching!