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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.
This course will build on concepts learned from Course I and will rely heavily on computer simulations to solve problems without closed-form solutions. Students will be taught the concepts of deterministic vs. stochastic systems (Gallager, 1996). This course will focus primarily on the statistical mechanics involved in describing nano-scale systems (Rieth, 2003). Boltzman statistics, Brownian motion, energy minimization, second law of thermodynamics, diffusion and self-assembly will all be covered. Stochastic based transport theory and self-assembly will also be covered. A course such as this is a critical component to any advanced undergraduate student or doctoral student, in that they will realize that the traditional classical deterministic models typically taught at the undergraduate level break down when one begins to consider nano-scale phenomena. This will be a valuable course for engineering students and medical students wanting to know how to model biophysical phenomena.
How early molecular winners affect our lives on a daily basis. This course will be directed to advanced undergraduate students and graduate students looking to apply the concepts of natural selection at work in the natural world with the evolution of human-made machines. Excerpts will be taken from Jared Diamond’s The Third Chimpanzee (Diamond, 1992), With-hold Rybczynski’s One Good Turn: A Natural History of the Screwdriver and the Screw (Rybczynski, 2000), A.G. Cairns-Smith’s Seven Clues to the Origin of Life (Cairns-Smith, 1990), and Henry Petroski’s The Evolution of Useful Things (Petroski, 1994).
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. SUMMARY OF COURSES TAUGHT, AND COURSES DEVELOPED
SYLLABI available upon request
Mathematics
matrix, tensor, vector notation, linear algebra, Markov processes, eigenvalue problems, analytical differential calculus, vector field calculus, heat transfer equations, fluid dynamics equations, elasticity equations ordinary differential equations, partial differential equation, Laplace transforms, Navier equations, variation of parameters, waves in elastic solids, series solutions, non-linear differential equations Fourier transforms, partial differential equations, numerical methods, optimization, stochastic processes, probability theory, and statistics Senior Design
Dynamics wrote and delivered lectures on Newtonian mechanics to Drexel’s pre-juniors worked with forty-five students on design projects to prepare them for their senior design class and to improve their technical communication skills. wrote and delivered lectures on Newtonian mechanics to Drexel’s pre-juniors worked with forty-five students on design projects to prepare them for their senior design class and to improve their technical communication skills. Materials led two recitations with approximately 30 students eachfacilitated online availability of course material Freshman Design design of an educational atomic force microscope. Students used LabView, SolidWorks and performed database research into the fundamentals of atomic force microscopy. Students submitted the completed version which includes an instruction manual for integration with the NSF-RET program. Students received the highest grade of their class and have a two online publications http://schc.sc.edu/nfb/NFBIssues.lasso and http://www.thenanotechnologygroup.org/index.cfm?content=79 covered basic principles of scanning electron microscopy and nanomanipulation with the ultimate goal of pushing the dexterity limits of the Zyvex L100. covered basic principles boat design evaluated the ability of nanoparticles to identify artifacts covered basic principles boat design explored alternatives to solid waste collection
Special Courses General Courses Taught introductory freshman course to facilitate transition to the university environment. Taught introductory freshman course to facilitate transition to the university environment. Courses Assisted
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Bradley Edward Layton
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