Mathematica-Based
Computer Laboratories for
the Enhancement Of a
Calculus Sequence
Mike O’Leary and Raouf
Boules Mathematics
Department
Towson University
ICTCM, 2000
Background (1)
Towson is a comprehensive university
located in the Baltimore metropolitan area
SAT mid range score of entering freshman
class in Fall 2000 is 500-590 (Verbal), and
510-590 (Math)
Main textbook in use: Stewart’s Calculus:
Early transcendental functions,
Brooks/Cole 1999
Background (2)
Audience: Mainly math, math education,
computer science, physics and chemistry
(lesser degree)
Semester system
Class meets for 4 hours per week for
lectures and one hour in a computer
laboratory
Philosophy (1)
Material supplements the mathematics
of an otherwise traditional course in
calculus, and is NOT a substitute for it
(more on this later)
Only small set of built-in functions used in
building small programs (Modules) for
graphical demonstration or to bypass
tedious repetitive calculations
Philosophy (2)
No prior knowledge of Mathematica
assumed
Material is based on interactive text (A
computer document from which symbolic,
numerical, and graphic tools can be invoked.
The results of these computations can be pasted
into the document so that each learner has an
individual record of his or her explorations)
Philosophy (3)
Students are encouraged to experiment
and make discoveries
Students may work in small groups but
submit a lab report individually
Students are expected to write answers,
many comments, observations,…etc
Mathematica Role: Black
Box or Teaching Tool (1)
History of Mathematica and its Use:
Wolfram: Born in 1959 and received his
PH.D. in Physics from Caltec in 1979
Began in 1979 constructing a CAS to solve
his own problems in physics
Mathematica released in 1988 by Wolfram
Research, Inc
Mathematica Role: Black
Box or Teaching Tool (2)
History of Mathematica and its Use
(cont’d):
Became popular first in the research fields of
science, engineering, and economics where it
was typically used as a black box to solve
complicated problems
Later it entered the scene of education as
people realized its potentials for
demonstrations and as its front end became
more user friendly
Mathematica Role: Black Box
or Teaching Tool (3)
Example 1: Using Newton’s method in
solving a nonlinear equation in a single
variable
Black box approach: use the command
FindRoot (This also uses Newton’s method)
Approach adopted: see next demonstration
Mathematica Role: Black
Box or Teaching Tool (4)
Example 2: Numerical integration
Black box approach: Use the command
NIntegrate (This uses a sophisticated
numerical adaptive quadrature algorithm)
Approach adopted: build a module to show
the graphical meaning of the tarpezoidal, and
Simpson’s rules; another assesses the error in
each as function of number of partitions and
asks for conjectures