The MTC Page


An NSF Supported Initiative

IPFW Division of Continuing Studies

 Department of Mathematical Sciences
Department of Physics


Physics-Based Calculus
A Workshop for Teachers
Monday, Tuesday, Wednesday, June 7,8,9, 2004.


IPFW Faculty Organizers
Adam Coffman
Timothy Grove
Peter Hamburger
Mark Masters

Photos from the 2004 Workshop.

Prof. Tim Grove's page
with a link to download the Sound Wave Analysis program.
Prof. Mark Masters' optical Fourier transform software
Prof. Peter Hamburger's Honors Calculus web site.
Prof. Adam Coffman's Notes for the Physics-Based Calculus workshop
10 pages, no pictures.
DVI PS PDF

Updated information for the 2004 workshop

The participant reimbursement checks should have arrived by now. Please contact Adam if you have not yet received yours.

FM Radio signal
An FM Radio Signal

  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 in a three-day workshop at Indiana University - Purdue University Fort Wayne. 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, computers, or art, may also be interested.

  • Prerequisites: Familiarity with trigonometric functions, and some previous exposure to first-year calculus. There is no physics prerequisite.
  • The program is in Kettler Hall, on the IPFW campus .
  • We meet from 8:30 AM to 4:00 PM on Monday, 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 and possible topics planned for the workshop:

  • Meet between 8:30 and 9:00 in Kettler 200.
  • Introduction to the Mathematics Throughout the Curriculum project
  • A review of concepts of velocity and acceleration, with ideas for low-cost physics demonstrations.
  • A review of wave concepts, such as frequency, amplitude, etc., with physics demonstrations.
  • Discussion of Fourier coefficients, demonstration of Maple software.
  • Demonstration of physics experiments, and hands-on experiments analyzing periodic motion, and resonance frequencies of masses on springs, with computer analysis.
  • Hands-on physics activities, using the computer to analyze sound data. Computer generated holography.
  • Discussion of issues in the high school calculus and science curriculum
  • New topics in high school-level calculus: early use of sequences and Taylor series, Fourier coefficients, the Binomial Theorem, Stirling's formula, Wallis' formula
  • The Fourier transform and its uses in computer science.

Registration

The 2004 workshop has finished, so registration is now closed. 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

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 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.

     


The 2004 Physics-Based Calculus workshop will be the fourth run of this program, following successful workshops in 2001, 2002, and 2003.
2003 Web site from the 2003 workshop.

Photos from the 2003 Workshop.

2002
2001


Department of Mathematical Sciences
Indiana University Purdue University Fort Wayne
phone: (260) 481-6821
BackTo the Department of Mathematical Sciences
BackTo the IPFW Division of Continuing Studies