first order ODEs
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Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
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Let's find the general solution!
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Let's use some initial conditions to solve for the particular solution.
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Another example with initial conditions!
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In this lecture, Professor Kagan continues to discuss the constitution of Athens. In particular, he explores the judicial workings of Athens. He describes in detail the effort of the Athenians to create a system of justice that would not only minimize tampering, in order to insure justice, but also maximize citizen participation. After this discussion, Professor Kagan comments on the role of women in Athens by looking at two types of sourc...more
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Kawasaki shares some of the qualities that he believes entrepreneurs, and everyone else, should have. In order to be a mensch, a person who is widely respected and trusted, one should help those who cannot be helpful in return, do the right thing in the right way, and pay back to society.
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Professor Freeman discusses what it meant to be a British colonist in America in the eighteenth century. She explains how American colonists had deep bonds of tradition and culture with Great Britain. She argues that, as British colonists with a strong sense of their British liberties, settlers in America valued their liberties above all else. She also explains that many Americans had a sense of inferiority when they compared their colonia...more
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Ringold talks about the fundamental differences between sole entrepreneurship in the academic setting versus entrepreneurship in an industry setting: a change in dynamics from a sole activity, to teamwork from different disciplines to solve fundamental problems. Industry has learned this long before the academic environment - that you need to bring people together from various industries and disciplines, with different skill sets to solve ...more
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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 di...more
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The exchanges in which stocks and other securities are traded serve an important function in finance. They bring together people interested in buying and selling securities in order to create a universal price. Brokers and dealers are also an important part of the system, their methods and standards are ultimately behind the success of the exchanges. Many information innovations have advanced the functioning of exchanges, going all the way...more
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This lecture is about optimal exercise strategies for callable bonds, which are bonds bundled with an option that allows the borrower to pay back the loan early, if she chooses. Using backward induction, we calculate the borrower's optimal strategy and the value of the option. As with the simple examples in the previous lecture, the option value turns out to be very large. The most important callable bond is the fixed rate amortizing mortg...more
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