Planned Course I:

Vectors and Tensors for Multiscale Biomechanics

This course will focus on Ordinary Differential Equations, Linear Algebra Methods, LaPlace and Fourier Transform Methods, and Statistics. All concepts used in the text are developed within the text itself and extended to challenging problems relying on a deep understanding of the concepts and offering the student a sense of satisfaction in having attained a thorough grasp of the content. The mathematics presented is applied across several disciplines including Hookean solids, Newtonian dynamics, Navier-Stokes fluid mechanics, and Special and General Relativity. This text also has excellent extensibility to computational mechanics as it relies heavily on linearization, and index notation.

 

Drexel has a strong reputation for design. Students begin design in their freshman year, and culminate their engineering studies with Senior Design project, frequently in conjunction with a local engineering firm. A focus of this course will be to evaluate a design’s relevance: Does it serve a purpose in today’s economic and social environment? Students taking this class will not only start to assess the natural progression of human-made artifacts, but will look at the rate at which we as a species are changing the natural landscape (Gleick, 1999) and where we may expect to go as a species (Kurzweil, 1999).

Optimization theory will be explored as will game theory. Additionally models for minimization of stress/maximization of strength within mechanical structures will explored with existing software and with codes devised by students within Matlab® and Mathematical®. The course itself will hopefully evolve into one in which students create virtual molecular worlds that have self-assembling structural and motor proteins that fight for survival on the nanoscale based on models such as those by (Hill, 1987), then evolve into larger structures that fight for the survival of their genes. The point will be made of how early molecular winners affects our lives on a daily basis (Dawkins, 1989), and will also teach the points of spending time up front to solve a problem that lies in the future. Other ideas that will be discussed are the limits of the sustainability of complexity. The sustainability of current information technologies will also be addressed to incorporate information theory (Yockey, 1992; Avery, 2003; Yockey, 2004) and the hypothesis that computation machines, like brains are merely nothing more than machines that turn data in to heat and information. One concept that student will also be exposed to that is unconventional for engineering students is that there is no goal of evolution. Survival is the only measure of success, not who is the fastest, smartest, strongest necessarily. A poignant example is that of the Coelacanth fish where a slow, average fish with probably little brain wattage has been able to survive for millennia without competition presumably due to its relatively low metabolism and ability to live in a niche environment. An overall theme of the class which will be explored is the apparent paradox that Life appears to be beating entropy at its own game. This will be addressed from a quantitative standpoint to look at how accrual of more tools or weapons (a machine or technology advantage) by one group can lead to a landslide victory over another. The prospect that there essentially is no way to escape the technological path we have “chosen” for ourselves will be explored as will the ethical question of whether “developing nations” really need to develop and what if any role our own “highly developed” society should take in this endeavor. Students will learn that there is perhaps some optimal level of complexity: if you are too complex you cannot sustain, too simple you are consumed.