Mt/CS 410 Mathematical Modeling - Fall 2002

Department of Mathematics & Computer Science
CARDINAL STRITCH UNIVERSITY
Sr. Barbara E. Reynolds, Ph.D.

Assignment 11: Population Growth and Dimensional Analysis

November 19, 2002

  • Read and study Section 10.1, pages 348 - 356. In this section, two different models for population growth are developed:

    1. the Malthusian model of population growth, developed by Thomas Malthus in the late 18th century, and
    2. a logistic growth model developed by Pierre-Francois Verhulst in the early 19th century.

      Even though each of these models was developed to study population growth (important to both biologists and sociologists), the models have come to have applications in a wide variety of fields. The exponential growth model is used in the fields of economics (particularly in the theory of interest) and physics (Newton's Laws of Heating and Cooling, as well as to study radioactive decay).

      You should be able to do the calculus to develop equations (10.7) and (10.11). You should also be able to explain why difference equations or derivatives are used to model various situations.

  • Read and study portions of Section 13.1: pages 443 - 445, Example 2, pages 448 - 450, and Table 13.1, page 449. In this section, a strategy for anlayzing a problem situation using the dimensions (or units) of the variables is used as a kind of check to see if the algebraic model develop makes sense.

    Attempt problems #1 and #3, page 450. You should be able to explain how you are using dimensions to verify whether or not the equation is dimensionally compatible.

  • Complete one of the choices for the Final Project. You may do this final project either individually or with a partner or small group. Each group or individual should plan to give a report on the project given to the class.

  • Think about whether you would like to participate in the international Math Modeling Contest, during the weekend of February 6 - 10, 2003. Participation in this contest is an intense experience. If you and your teammates are able to submit a complete solution to the contest problem, this can be mentioned as a significant academic accomplishment in a personal essay, on a resume, or in a job interview. I am willing to serve as faculty advisor for one or two teams of up to three students each. Each team must register by Thursday, February 6, but realistically, I need to know if you are interested in this contest by the start of the spring semester, January 21.

    Return to Sr. Barbara E. Reynolds Home Page.
    Return to course list for 2002 -- 2003.
    Go to Mt/CS 410: Mathematical Modeling Syllabus.
    Return to Mt/CS 410: Mathematical Modeling Assignments.
    The easiest way to contact me is to send an email message to Sr. Barbara E. Reynolds.
    This page was updated on November 16, 2002.