Nash Equilibrium
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Professor Sylvia Ceyer discusses the classification of acids and bases as they are defined by Arrhenius, Bronsted-Lory, and Lewis acid/base. The pH function (and pOH function) are defined as they relate to the strength of acids and bases (in water). Professor Ceyer then runs through the types of acid-base problems and concludes by discussing equilibrium involving weak acids.
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Professor Sylvia Ceyer continues her discussion of acid-base equilibrium, diving into buffers. The lecture concludes with the Henderson-Hasselbalch equation and its use in designing a buffer.
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Professor Sylvia Ceyer discuses titrations involving a strong acid and a strong base. Defining the point and equivalence and the end point. The lecture continues with a focus on calculating points on a pH curve, specifically calculating pH before the equivalence point, calculating volume of HCl needed to reach equivalence point, and calculating pH after the equivalence point. Finally, Professor Ceyer discusses characteristics of...more
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Breeding strategies differ both among males and females of the same species as well as among different species. The difference in breeding strategies among members of the same species can usually be linked to frequency dependence. If the species is at evolutionary equilibrium, the relative fitnesses of these different strategies will be identical. Differing strategies have been found at the level of the gamete as well as at the level of...more
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We first discuss Zermelo's theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we...more
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We continue the idea (from last time) of playing a best response to what we believe others will do. More particularly, we develop the idea that you should not play a strategy that is not a best response for any belief about others' choices. We use this idea to analyze taking a penalty kick in soccer. Then we use it to analyze a profit-sharing partnership. Toward the end, we introduce a new notion: Nash Equilibrium.
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After discussing the classic determination of the heat of atomization of graphite by Chupka and Inghram, the values of bond dissociation energies, and the utility of average bond energies, the lecture focuses on understanding equilibrium and rate processes through statistical mechanics. The Boltzmann factor favors minimal energy in order to provide the largest number of different arrangements of "bits" of energy. The slippery concept of...more
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Professor Sylvia Ceyer discusses the nature of chemical equilibrium as it relates to free energy, the reaction quotient, and the relationship between K and Q. The meaning of K is further clarified and the external effects on K are identified, from adding and removing reagents to changes associated with the Principle of Le Chatelier.
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Professor Sylvia Ceyer continues her discussion on chemical equilibrium and external effects such as a change in volume, adding inert gas, and a change in temperature. Parameters are set for maximizing the yield of a reaction, and the Principle of Le Chatelier's is returned to. Hemoglobin is used as an example involved in a series of equilibrium reactions in response to oxygen pressure.
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The form of medicine that arose in fifth-century Greece, associated with the name of Hippocrates and later popularized by Galen, marked a major innovation in the treatment of disease. Unlike supernatural theories of disease, Hippocrates' method involved seeking the causes of illness in natural factors. This method rested upon an analogy between the order of the universe and the composition of the body's "humors." Health, on this view, was...more
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
