Mathematics Throughout The Curriculum Links
The MTC Page
IPFW
Honors Calculus

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.
The 2001 Workshop has
concluded! Participants should expect some materials and
reimbursement to arrive in the mail.
PHOTOS FROM THE
WORKSHOP
Schedule
 The program is in Kettler Hall, on the IPFW campus.
 Friday, May 4: start at 2:00, break at 4:00, stop at 6:00.
 Demonstration of physics experiments: masses on vertical and
horizontal springs.
 Demonstration of software for physics, analyzing data from
force and position detectors.
 Discussion of Fourier coefficients, demonstration of Maple
software.
 Saturday, May 5: start at 9:00, lunch at 12:00, break at 3:00,
stop at 5:00.
 Demonstration of physics experiments: equipment for analyzing
sound waves and vibrations, resonance frequencies of masses on
springs, laser optics, the Michelson apparatus, and the Doppler
effect.
 Presentation on honors research in geology and mathematics, by
IPFW student Alex James.
 Handson physics activities, using the computer to analyze
motion and sound data.
 Demonstration of internet software for mathematics 
available on Professor Pan's Java Technology
Laboratory web
site.
 Discussion of applications of Fourier analysis in biology, and
the structure of Professor Hamburger's Honors Calculus course.
 Sunday, May 6: start at 9:00, break at 11:00, stop at 12:00.
 Discussion of complex numbers and the mathematical derivation
of the Fourier transform.
 Discussion of issues in the calculus curriculum.
One of the aims of the Mathematics Throughout the Curriculum
project is the "dissemination" of its ideas. So, the project will
provide funding for some (up to 30) workshop participants, in the
amount of $150.
Registration
Registration is closed, but if you have questions about this
workshop, please contact Professor Hamburger (Hamburge (at)
ipfw.edu) or one of the organizers.
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.
