Explorations for
Multidifferential Integral Calculus
and Vector Analysis

The following items are a collection of mathematical explorations developed by Eric Carlen, Evans Harrell, and Jim Herod. Some are formatted with Maple V. Release 4, some with Mathematica 2.2.2, and some incorporate Java Applets. They are grouped below depending on the type of software used. In addition, this page contains some links to further material of interest to mathematics students.

This page and its links contain copyrighted materials by Eric Carlen, Evans Harrell, Jim Herod, and others. Unrestricted use for classroom purposes by Georgia Tech students and faculty is permitted, provided that the contents are unaltered, properly acknowledged, and contain this copyright notice. Casual use is permitted off campus with the same restrictions. If you are interested in regular off-campus use, please write us.

Maple-based lectures by James V. Herod

Mathematica-based lectures by Evans M. Harrell II

Class notes by Eric Carlen

The page at this link contains lectures covering material throughout the course, including interactive applets using the Java programming language.

Explorations for
Introductory Differential Equations

  • Flow Across Membranes. This worksheet models the flow of a fluid through a cylinder whose sides are a thin walled membrane. The membrane permits the absorption or release of a solute. Whether the solute is absorbed or released depends on the difference in the concentration in the cylinder and in the surrounding medium. With the assumption that the cylinder enters regions that alternately have higher or lower concentrations than the fluid in the cylinder, we seek a description for the concentration in the cylinder.
  • Flow Across a Membrane with Con-current or Counter-current Flow. Imagine two tubes, one with a smaller radius and contained in the other. Also, imagine the walls of the smaller tube being a membrane permeable to a solute that is dissolved in a fluid flowing through the smaller tube. A "cleaning fluid" flows in the larger tube. This worksheet explores the difference in the efficiency in removing the solute from the inner fluid depending on whether the fluids flow in the same or opposite directions.
  • Coffee With the President . The President and the Prime Minister have coffee together. One of them pours in cream immediately, the other waits ten minutes. Which has the cooler cup of coffee? This problem is classical in undergraduate differential equations. A slight twist is added to the problem because of a bright Georgia Tech graduate serving as a Presidential Aide.
  • U. S. Census Data: Exponential or Logistic . Two simple models for population growth are exponential growth and logistic growth. In this worksheet, we examine the U. S. Census Data during this century and devise methods to construct an exponential model and a logistic model for this data. For both, a least squares fit for a modification of the data is used.
  • Graphical Solutions for Two Dimensional Differential Equations . Quick, graphical solutions for a two dimensional system of differential equations is only a point and click away. The program is fast, the interface is neat, the learning curve is "flat"! What more could you want? (Point and Click here!)

    • Some external links

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