APPLETS AND PROJECTS FOR CALCULUS IV

Page Contents

  • APPLETS: The applets in the fast-downloading jar file format
  • APPLETS:The applets in the unarchived format required by Navigator 3
  • EXPERIMENTS AND PROJECTS:A collection of projects and experiments to be done with these applets

    • The applets in jar files
    Use these links if you are using Netscape Navigator 4, or another browser that understands the "archive" tag, and your downloads will be faster.
  • Applet on the Lagrange multipliers method for solving constrained optimization problems.
  • Applet on the Newton-Raphson method for finding roots in two variables.
  • Applet on two dimension integration in Cartesian coordinates with Riemann sums.

    • The applets in unarchived form
    Use these links if you are using Netscape Navigator 3, or another browser that does not understand the "archive" tag, and the applets will be downloaded the old-fashioned way: one class at a time.
  • Applet on the Lagrange multipliers method for solving constrained optimization problems.
  • Applet on the Newton-Raphson method for finding roots in two variables.
  • Applet on two dimension integration in Cartesian coordinates with Riemann sums.

    • Projects and experiments for use with these applets
    The following links are to pdf files outlining mathematical experiments designed to be done with these applets. Since several of the applets are on closely related subjects, some of these experiments involve the use of two or more of the applets, while others just use one.

    Section Contents

  • Experiments with Lagrange multipliers in two dimensions
  • Experiments with Newton's method in two dimensions
  • Experiments with Riemann sums in two dimensions

  • Experiments with Lagrange multipliers in two dimensions

     This project is designed to lead to a geometric understanding constrained optimization problems in two dimensions.

    Project resources

  • The questions to be explored and answered.
  • Notes and hints on use of the applets for studying these questions.
  • Notes on the theory behind the questions.

  • Experiments with Newton's method in two dimesions

     This project is designed to lead to a deeper understanding of linearization in two variables and gradients. The basic idea behind Newton's method in any number of dimensions is to replace exact but hard non-linear eqautions with approximate but easy linear eqautions. In several variables, there are several ways to do this. Two of these are explored here. The goal is to help students get beyond the formulas, and to see Newton's methos as an example of the power of being able to linearize problems.

    Project resources

  • The questions to be explored and answered.
  • Notes and hints on use of the applets for studying these questions.
  • Notes on the theory behind the questions.

  • Experiments with Riemann sums in two dimensions

     This lab is designed deepen student's understanding of multiple integrals as Reimann sums. In the process, they should get a feel for the terrible abount of computation that goes into approximating a two dimensional integral to a given degree of accuracy, as compared to the relatively small amount for one dimensional integrals. Students shouls aquire an appreciation for being able to exactly reduce a two dimensional integral to a one dimensional integral before turning to numerical integration.

    Project resources

  • The questions to be explored and answered.
  • Notes and hints on use of the applets for studying these questions.
    • Eric A. Carlen (send message)