Calculus? Each of us has a different reaction. Even if you're interested,
the details can be intimidating, leaving you with a negative impression and
without an understanding of what makes the subject interesting and important. This app introduces some key ideas while avoiding the details. Each idea has an interactive graphic to illustrate it. You don't need to
know algebra, although if you are familiar with graphs, the ideas will be clearer.

The ideas are introduced graphically and interactively, without the tedious
details needed for a thorough study of the subject. Info text helps to explain each graphic. It is intended to be
interesting and fun for those with little or no math background, or even as a
study aid for Calculus students.

*Try it for free, and enjoy!*

Here are the app screens:

Speed and distance are familiar ideas. Think of a car or bicycle: the more speed you
have the more distance you cover. Travel for one hour at 20 MPH and you go 20 miles,
while at 40 MPH you go 40 miles. On this page, the Speed slider is like a combination
speedometer and gas pedal, while the Distance slider is like the car. The Speed
slider both controls and displays the speed of the Distance slider.

Here we look at the idea of slope, and its relationship with speed.
The top of the triangle has the slope of interest, and the other two sides of the
triangle have been animated with little arrows. The bottom arrows run across at a
constant speed, and are linked to the arrows moving upward. The speed of the arrows
moving upward depends on the slope. The higher the slope, the faster the vertical
arrows. Their speed is proportional to the slope. The slope is also shown by the
bar indicator and a number.

We know what a slope is, but what about curves, where
there isn't a constant slope? What we do is to consider a section of the curve, and
shorten this down near to nothing. Over this short section we simply place a line from
one end to the other. If the curve is smooth enough, this line gets closer and closer
to the curve. If you were to magnify this you would see that a very short section of the
curve is essentially a line. We can make the line as short as we want, and the slope gets closer and closer
to a certain value, the slope-at-a-point, called the derivative at that point.

What we did with one point can be done with an entire curve by dividing it up into more
and more shorter segments. The slope of each segment in the lower graph is shown in
the top graph as the height of a horizontal segment. The height represents the value
of the slope on the lower graph. It might seem strange, but as the segment sizes
shrink to zero, these height segments actually merge into a continuous curve, called
the mathematical derivative. The value (height) on any point on this top graph is the 'slope'
at the corresponding point on the bottom curve.

Here we have a curve that we can
adjust using the round markers. The curve is reconfigured to go through the markers.
While we adjust them we can also see the graph of the derivative (green).The derivative will be
above or below zero at points where the adjustable curve is rising or falling.
You can move two markers at once, or more if your phone or tablet allows it.