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Mathematics Throughout The Curriculum Links
The MTC Page
IPFW Honors Calculus
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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.
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| 2002 |
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| 2001 | |
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To the Department of Mathematical
Sciences
