# Tangent Lines and Areas Under the Curve (Calc101)

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### PRODUCT DESCRIPTION

KineMath Calc101 helps teachers and students of mathematics
with the exploration of the basic concepts of calculus.
Its clear and intuitive user interface provides an
unparalleled representation of tangent lines, derivatives,
anti-derivatives, areas under the curve and integrals.
These are the topics that constitute the core foundation of
any introductory calculus course.

KineMath Calc101 exploits the versatility and touch
capability of the iPad to bring the beauty of mathematics
to the fingertips of teachers and students of calculus.
The App provides a dynamic way for the user to interact
and explore these ideas, providing an amazing visual
representation of the concepts studied.

The Tangent Line Application

The Tangent Line application provides the mechanics
to explore the functions that are most widely used
in a high school course. The main slider scans the
function while having options to plot a Track Point
on the function, its tangent line at that particular
point and the derivative of the function in question.
All of these are controlled by switches that can
be turned ON and OFF. As was the case in the previous
KineMath app, all functions have a set of parameters
that are controlled by sliders.
Pinching and panning gestures are of course available,
in order to give the user a sense of control over the
plots that are being studied. Pinching does work
on independent directions, allowing for full manipulation of the functions.
The equations of the tangent line and derivative
function do appear when their switches are turned ON,
providing a dynamic equation that listens to every
change of the main parameters.
All sliders in this app can be customized to vary
their range or to pick specific values that might
otherwise be difficult to reach.
The main equation of the function that is being
explored will always appear in green.
Pressing the camera icon does save the graphing view
as an image to the main photo library of the iPad.
This feature allows the user to export images for many
other purposes, like email or print.

The Riemann Sum Application

The Riemann Sum application is a typical exploration
of left, right, midpoint and trapezoid sums. The user
has the ability to vary the values of “a” and “b”,
while having the freedom to pick up to 50 elements
or subdivisions. Recall that this application
is intended as an exploration to facilitate the
understanding of Riemann Sums. Typically, only a few
rectangles or elements are needed to visualize these
ideas.
Calc 101 does have some computation ability: It
calculates the corresponding areas for each sum, given
certain value of “n”, the number of subdivisions.
The bottom left of the screen shows a table with all
the corresponding values, including Simpson’s rule,
which is just a weighted average of the midpoint and
trapezoid rule.
The “Detail Areas” button at the bottom of the screen
provides a popover view with a table that shows the
values of areas of all the individual subdivisions for
each sum. Tapping one of these cells will highlight
the corresponding region in the graph.
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Teaching Duration
Lifelong Tool

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