Mission and Goals
Recently, under the leadership of Dean Daniel Larson (PSU) and Dean Jiping Zhang (PKU), a substantial collaborative agreement was signed between the Eberly College of Science at PSU and four different colleges and schools (mathematics, physics, chemistry and life science) at PKU to establish an international exchange program for students, postdocs, and faculty from both institutions. We are proposing a PKU-PSU undergraduate summer course, to be held in 2008 at PKU, as a first step towards building such an international undergraduate training program.
The main component of the program is a new course on differential equations (DE). The novel aspect of this course is to present the theory, numerical approximations, and applications of DEs altogether. On one hand, theoretical results of DEs are an essential part of the process of constructing and analyzing corresponding numerical schemes. As such, computational methods are best taught in unison with the related DE theory, which will at the very least need to be reviewed, but are often not covered thoroughly enough, in a numerical analysis class. On the other hand, computer simulations for DEs provide a convenient way to access and visualize solutions of DEs, especially for cases where the analytical solutions are not readily available.
Therefore we plan to offer a new undergraduate course, entitled “Analytical and numerical methods for differential equations". The topics of this new course will include basic numerical techniques, differential equations, analytical methods, finite difference and finite element approximation schemes, and various science and engineering applications modeled by differential equations. The later topic will demonstrate to students the relevance of the proposed mathematics topics in science and engineering and find their niche in scientific research. In addition to the classroom material, group projects, led by faculty participants, will be assigned. This training of students to work with diverse teams is another invaluable component of the program. We are also planning several culture-related lectures and activities for the students from PSU to expose them also to the ethnic culture and customs of China.

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