Instructional Laboratory for Undergraduate Mathematics Majors

Hien T. Tran

Center for Research in Scientific Computation
Department of Mathematics
Box 8205
North Carolina State University
Raleigh, NC 27695

tran@control.math.ncsu.edu,

Grant Number: DUE: 9751284

For the past three years, we have developed (on a small scale 10-15 students) a modeling course based on fundamental physical processes: heat flow, wave propagation, fluid and structural dynamics. Among the specific topics covered in the course were thermal imaging and detection, dynamics properties (stiffness, damping) of structures such as beams and plates, acoustics and fluid transport. The course, at a level appropriate for juniors, seniors and first year graduate students in the mathematical sciences, has been an unqualified success and is being expanded from a one semester trial course to a two semester regular course sequence.

A major innovative component of the course has been the exposure of students to specific laboratory experiments, data collection and analysis. As usual in such modeling courses, the pedagogy involves beginning with first principles in a physical, chemical or biological process and deriving quantitative models (partial differential equations with boundary conditions, initial conditions, etc.) in the context of a specific application such as thermal nondestructive damage detection in structures, active noise suppression in acoustic chambers, smart material (piezoceramic sensing and actuation) structures vibration suppression, and fluid transport in thin film vapor deposition reactors. The students then use the models (with appropriate computational software - some from MATLAB, some from routines we have developed specifically for the course) to carry out simulations and analyze experimental data. The students are exposed to experimental design and data collection through laboratory demos in certain experiments and through actual hands-on experience in other experiments. This entails multiple lab visits during a one semester course.

One of the difficulties during the past three years has been the necessity to use several different laboratories (thermal, acoustic, mechanical/structural) throughout the semester. These laboratories were not under our scheduling control (we used labs at NASA Langley, local industries, and even other universities in the case of some of the piezoceramic based vibration experiments) and there was some mild stress involving scheduling presentation of basic material in the courses around lab opportunities. To bring this pedagogy to a wider group of students, we are developing a dedicated laboratory with support provided by the NSF under the instrumentation component of the ILI program. This laboratory is not a research laboratory in the usual sense since its main purpose will be to support the advanced applied mathematics courses.

In this presentation, we will detail several specific areas of experiments (thermal, acoustic, and mechanical vibrations) which have been developed to support the above mentioned year-long modeling course. In addition, we will discuss how these experiments can provide demos and hands-on data collection to support more traditional applied mathematics courses such as ordinary differential equations and partial differential equations.


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