Interactive Learning in Calculus and Differential Equations with Applications

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. The project was funded through a National Science Foudation Instrumentation and Laboratory Improvement grant, number DUE-9351896. 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 coinvestigators.
• 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.

Check back later at this location for more Mathematica notebooks relating to calculus, ordinary differential equations, and partial differential equations. Some of the topics covered are:

• Finding Areas with the Gauss-Green Formula,
• Newton's Method and Fractals,
• Vibrating Drumheads
• Some Multivariable Calculus Ideas
• Multivariable Calculus Ideas II
• Orthogonal Curvilinear Coordinates
• Basic Complex Numbers for Applied Mathematics
• The Drag Force on a Sphere
  (This notebook predates our project, but it fits in, so we are including it anyway)

In order to disseminate these Mathematica notebooks, one of the PIs in this grant wrote a program, mma2html, to convert Mathmematica notebooks to HTML documents. This program is available to the public.

Presentations:
1. "Mathematica in the Classroom", Francisco Alarcon and Charles Bertness, Lock Haven University, February 21, 1994.
2. "IUP's Mathematica Network", Rebecca Stoudt, poster session on "Computer Laboratories in Mathematics Education", American Mathematical Society/Mathematical Association of America Joint Meeting, Cincinnati, Ohio, January 1994.
3. "Restructuring the First Differential Equations Course for Mathematics and Science Majors using Mathematica", Francisco Alarcon, in the MAA session "New Methods for Teaching Ordinary Differential Equations", American Mathematical Society/Mathematical Association of America Joint Meeting, Cincinnati, Ohio, January 15, 1994.

Francisco Alarcon, Don Balenovich, Charles Bertness, Gerald Buriok, Dan Burkett, Arlo Davis, H. Edward Donley, Gary Stoudt, Rebecca Stoudt

Related Topics

• Imperial College's Transitional Mathematics Project
• The Consortium for Ordinary Differential Equations Experiments

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