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Interactive Learning in Calculus and Differential Equations with Applications

Gary Stoudt
Organization: Indiana University of Pennsylvania
Department: Mathematics
H. Edward Donley
Organization: Indiana University of Pennsylvania
Department: Department of Mathematics
URL: http://www.ma.iup.edu/people/hedonley.html
Education level


This project integrates discover-based learning with Mathematica into the calculus sequence, Differential Equations, and Advanced Mathematics for Applications courses. These courses form a four-course sequence for mathematics and science majors.

  • Calculus&Mathematica by Bill Davis, Horatio Porta and Jerry Uhl (Math Everywhere, Inc.)
  • Differential Equations with Boundary-Value Problems by Dennis G. Zill and Michael R. Cullen (Brooks-Cole Publishing Company)
  • Introduction to Applied Mathematics by Gilbert Strang (Wellesley-Cambridge Press)

Selected Mathematica Notebooks:
  • Finding Areas with the Gauss-Green Formula
  • Newton's Method and Fractals
  • Vibrating Drumheads
  • The Drag Force on a Sphere

The Mathematics Department at Indiana University of Pennsylvania (IUP) established a computerized learning environment, consisting of a classroom with 31 Macintosh Centris 650s and a laboratory with 12 Macintosh LCs, all equipped with Mathematica. Mathematica's notebook feature enables science students to actively learn calculus and differential equations with guided discovery and exploration.

IUP's project has several significant attributes:
  • The Mathematics Department is fully implementing this curriculum in all sections of its science calculus sequence and in the two-semester differential equations sequence.
  • Eleven faculty, comprising approximately one third of IUP's mathematics faculty, are co-investigators.
  • The curricular revisions are being coordinated with the science departments at IUP, who are also integrating active learning and technology in their courses. This collaboration, based on common pedagogical goals and software, will bring more scientific applications into mathematics courses and strengthen the use of mathematics in science courses.
  • All students in the Mathematics Department are involved. Mathematics and Applied Mathematics majors are required to take Differential Equations, and Mathematics Education majors have a unit devoted to the project in the teacher preparation course, Computers and Calculators in Secondary Mathematics.
Advanced Mathematics for Applications is more fully described at http://library.wolfram.com/courseware/index.cgi?id=77

*Mathematics > Calculus and Analysis > Calculus
*Mathematics > Calculus and Analysis > Differential Equations