Title                Visual Demonstrations for Calculus Using Mathematica

Course           Calculus II – Math 2414, Fall 2009

Students        Mito Are, Recipient of HI-TECCC Scholarship awarded in Spring 2011

Daniel Relix

Summary:

This set of demonstrations illustrates some concepts of Calculus II using built in Mathematica functions that allow user control and manipulation.

Surface Area of a Solid of Revolution:
This Demonstration shows the approximation steps that lead to the derivation of the general formula for the surface area of a solid of revolution about the x-axis. The first view shows that the surface is a union of bands like the one swept out by the arc PQ. The second view shows how the line segment joining P and Q sweeps out a frustum of a cone. The last view shows the dimensions associated with arc and line segments PQ.

Strips of Equal Width on a Sphere Have Equal Surface Areas:
On a sphere, strips of equal width have equal surface areas. The sphere is generated by revolving the semicircle about the x axis. The slices can be selected by the user.

Radioactive Decay of Five Elements - Time Dependence of Remaining Mass:
In this Demonstration, you can select the decay time and initial mass for one of five radioactive elements. The remaining mass of the element is then shown as a function of time.