Catch the Waves to Calculus
Integrated Calculus and Analytical Geometry

Target Audience

Undergraduates with at least college algebra and trigonometry

Course Description

A two-semester calculus sequence with undergraduate research projects in a wide variety of disciplines. The focus is on the mathematical foundation of the Fourier series, the Fourier and the inverse Fourier Transform, and the theoretical background of the Fast Fourier Transform.

Fourier series and Fourier and inverse Fourier Transforms are used in many higher-level mathematics, science and engineering classes, such as

• partial and ordinary differential equations,
• physics, chemistry, biology,
• medicine, communication science, photography, linguistics

The Fast Fourier Transform method is used in many areas of research and in industry:

• In physics: solid-state physics, quantum mechanics, and wave mechanics
• In chemistry, biology, and geology
• In X-ray crystallography
• In engineering: devices engineered on the basis of Fast Fourier Transforms are used in the design and construction of smooth-running cars, trains, and airplanes. These devices use Fast Fourier Transforms to eliminate noises and vibrations.

In individual projects, the students conduct research on actual applications from their own area of studies. They are supervised jointly by the mathematics instructor and an instructor from the other discipline.

Course Web Page

For a complete description of this course, go to Catch the Waves to Calculus

For Further Information, Contact ...

• Peter Hamburger, Department of Mathematical Sciences, Indiana-Purdue University Fort Wayne
  e-mail hamburge@ipfw.edu