Proposed Activities and Schedule
The proposed REU would begin on Monday, June 29 (with students arriving Sunday, June 28) and end on Wednesday, August 12, for a total of six and a half weeks.
Proposed Activities:
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Activity/
Support
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Activity/Support Description
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Short Course in ODEs
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This course will focus on a review (since the students have already taken a course in differential equations) of the more relevant techniques to solve ODEs of first order and second order related to our research problems.
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Mini Course in nonlinear ODEs
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This course will focus on the study of the solutions for Riccati equations both homogeneous and nonhomogeneous, with variable coefficients and their applications.
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Short Course in PDEs
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This course will focus on solutions for the wave, heat and Schrödinger equations in the real line. Emphasis on traveling wave and self-similar solutions will be given. Finally, Anzats techniques appropriate for our two research problems will be taught.
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Research Seminar
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The PI will provide (for discussion) his published results on explicit solutions for evolutions equations using the Riccati equation with variable coefficients, along with the multiparameter approach, and his expectations on the interpretation of the dynamics of the explicit solutions.
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Graduate school preparation
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This support will consist of workshops and seminars such as GRE preparation, technical writing, and graduate school success strategies. Some of these workshops are offered pro bono through the English Writing Center, and some of these seminars will be hosted by the UPRM Chemical Engineering Department REU in Reconfigurable and Multifunctional Soft Materials http://inqu.uprm.edu/research/nsf-reu), an NSF-funded summer REU approved for the next three years.
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Computer Lab
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Students will be given instruction and practice in the use of MATLAB and Mathematica. Emphasis will be placed on solving ODEs and PDEs and also graphing their solutions with these packages. These skills and practice will consequently be applied to the research problem and publishable paper. The computer lab will be monitored by a graduate student.
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Tutoring
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A graduate student will be available in the evenings for group and one-on-one tutoring for the REU participants throughout the REU experience. The graduate student will also offer support and advice for them as prospective graduate students.
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