Mathematics Throughout The Curriculum Links
The MTC Page
IPFW
Honors Calculus

Invitation: We
invite teachers of Mathematics or Science, at the high school or
college level, to participate. The theme of the workshop will be
Fourier Analysis, a branch of mathematics which has many applications,
and which can be incorporated into a physics or calculus curriculum.
Teachers in other subjects, such as music, may also be interested.
 The program is in Kettler Hall, on the IPFW campus (link to Campus Maps).
 We meet from 9 AM to 4:30 PM on Tuesday and Wednesday,
with breaks during the day, and lunch provided for participants.
 Visitor Parking is free in the "B" spaces, near Kettler hall.
PHOTOS FROM THE 2002
WORKSHOP
List of activities for the workshop:
 Meet between 9:00 and 9:30 in Kettler 200.
 Introduction to the Mathematics Throughout the Curriculum project
 A review of frequency, amplitude, etc., with a physics
demonstration.
 Discussion of Fourier coefficients, demonstration of Maple
software.
 Demonstration of physics experiments, and handson experiments
analyzing pendulum motion, and resonance frequencies of masses on
springs, with computer analysis.
 Discussion of complex numbers and the mathematical derivation
of the Fourier transform.
 Presentation of a student research project, by an IPFW
undergraduate who has finished the Honors Calculus sequence.
 Handson physics activities, using the computer to analyze
sound data. Computer generated holography.
 Introduction to the Fast Fourier Transform and computational
issues.
 Discussion of issues in the high school calculus and science
curriculum
One of the aims of the Mathematics Throughout the Curriculum
project is the "dissemination" of its ideas. There is no fee for
registration, no text or equipment is required, and this workshop is
not offered for college credit. Subject to available funding,
participants will receive $100 reimbursement for attending both days
of the workshop.
Registration
Registration is closed because the workshop is over. If you
have questions about the workshop, you can find some contact
information if you PRINT OUT THIS
FORM, or just send email to Professor Hamburger at Hamburge (at) ipfw.edu.
Lodging
Participants from out of town are responsible for making their
own arrangements for a place to stay.
Some Applications of Fourier Analysis in Physics
Here are some brief descriptions of physics projects where both
the theoretical predictions and the experimental data can be analyzed
using Fourier methods.
 Force and Motion; Vibrations and Spring Systems.
Monitoring the force exerted on a probe at the upper support we can
determine the modes of vibration in coupled oscillators.
A graph of experimental data and its
Fourier Transform (79KB)
 Building vibration analysis.
Using speakers and a simple vibration probe we can monitor and
determine the modes and frequency of vibration.
A photo (104KB) of the monitoring device
 Sound analysis.
The human voice and musical instruments can be examined using
Fourier transforms to determine the frequency components and their
relative phases.
Waveform of a Reed.
Fourier Transform of above waveform
 Light : Double slit interference, Interferometers
Splitting light such that the two parts travel different path
lengths produces interference. The interference pattern can be
considered as a Fourier transform on the incident light – dependent
upon the wavelength of the light and the path difference between the
two paths.
A photo (356KB) of the laser experiment
A graph with a curve and data points
 Light : Fourier Optics
Lenses, when arranged appropriately, take a twodimensional Fourier
transform of an object. This process can be used for image processing
and filtering. This same process can be employed to produce
calculated holograms.
The 2002 PhysicsBased Calculus workshop will be the second run of
this program, following a successful workshop in 2001.
Here's the web site from the workshop in
2001.
PHOTOS FROM THE
2001 WORKSHOP
