Undergraduate Research Projects in Vector Analysis at Hostos:First-place Awarded to CSTEP Students

Alexander Vaninsky, Professor
Mathematics Department

 

The winning project at 25th annual Collegiate Science and Technology Entry Program (CSTEP) state-wide student conference was one out of the two projects accomplished under the supervision of Professor Alexander Vaninsky from the Mathematics Department, Hostos CC. Both projects were accomplished by the students pursuing associated degrees in engineering during their sophomore year.

Participants were selected on the voluntary basis among the students who expressed interest in mathematics and were willing to study beyond the traditional curriculum requirements. By the time of joining this research, all of the students were either taking the calculus III course (multiple integrals and the Green’s, Stokes’ and the Divergence theorems) or continued their mathematics preparation taking courses in linear algebra with vector analysis or differential equations. During the project, the participants were required to study relevant theoretical material and prepare a collection of solved problems. All of them also joined the CRSP/CUNY Research Scholars Program (pronounced, crisp) or STEP Hostos programs and received supporting scholarship.

Both projects included theoretical and application parts. Project #1 was to obtain an explicit formula for the curvature of a curve in plane defined implicitly in rectangular or polar coordinates. This project was nominated but was not the winner. Project #2 – the winning one – was aimed to develop an alternative procedure for finding potential function for a vector field in space based on simultaneous integration. Applications part of the Project #1 included finding critical – from the normal acceleration point of view – points on the trajectory of a moving body. Solutions to this problem may be of interest for the developers of the software for the driverless cars. Results obtained in the Project #2 may be used as a teaching tool for the vector analysis course.

A working paper summarizing the obtained results co-authorized by Professor Vaninsky and participating students was posted on the CUNY repository website http://academicworks.cuny.edu/pubs/.

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