An NSF Supported Initiative

IPFW Faculty Organizers
Adam Coffman
Timothy Grove
Peter Hamburger
Mark Masters

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.

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 hands-on 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.
• Hands-on 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 e-mail to Professor Hamburger at Hamburge (at) ipfw.edu.

Lodging

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 two-dimensional 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.

   

Here's the web site from the workshop in 2001.

PHOTOS FROM THE 2001 WORKSHOP