Dimensional Analysis
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Recap: Conjugate Gradient Method, Recap: Krylov Subspace, Spectral Analysis Of Krylov Sequence, A Bound On Convergence Rate, Convergence, Residual Convergence, CG Algorithm, Efficient Matrix-Vector Multiply, Shifting, Preconditioned Conjugate Gradient Algorithm, Choice Of Preconditioner, CG Summary, Truncated Newton Method, Approximate Or Inexact Newton Methods, CG Initialization, Hessian And Gradient, Methods, Convergence Versus...more
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Professor Blight narrates the momentous events of 1857, 1858, and 1859. The lecture opens with an analysis of the famous Lincoln-Douglas debates of 1858. Next, Blight analyzes the Dred Scott decision and discusses what it meant for northerners--particularly African Americans--to live in "the land of the Dred Scott decision." The lecture then shifts to John Brown. Professor Blight begins by discussing the way that John Brown has been...more
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Professor Kleiner traces the evolution of Roman architecture from its beginnings in the eight-century B.C. Iron Age through the late Republican period. The lecture features traditional Roman temple architecture as a synthesis of Etruscan and Greek temple types, early defensive wall building in Rome and environs, and a range of technologies and building practices that made this architecture possible. City planning in such early Roman...more
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In this lecture we move from present values to dynamic present values. If interest rates evolve along the forward curve, then the present value of the remaining cash flows of any instrument will evolve in a predictable trajectory. The fastest way to compute these is by backward induction. Dynamic present values help us understand the returns of various trading strategies, and how marking-to-market can prevent some subtle abuses of the...more
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Continued Discussion Of Fourier Series And The Heat Equation, Transition From Fourier Series To Fourier Transforms (Periodic To Nonperiodic Phenomena), Fourier Series Analysis And Synthesis; Relation To Fourier Transform And Inverse Fourier Transform, Fourier Series/ Coefficients With Period T, Spectrum Picture For Fourier Series With Period T, Effects Of A Change In T, The Complications Of Finding The Fourier Transform By Letting T Go To...more
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Continuing the examination of molecular orbital theory as a predictor of chemical reactivity, this lecture focuses on the close analogy among seemingly disparate organic chemistry reactions: acid-base, SN2 substitution, and E2 elimination. All these reactions involve breaking existing bonds where LUMOs have antibonding nodes while new bonds are being formed. The three-stage oxidation of ammonia by elemental chlorine is analyzed in the...more
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The Industrial Revolution was for a long time treated as a decisive break in which some countries, specifically England, innovated and progressed rapidly while others were left behind. This type of analysis leads many historians to overlook the more gradual process of industrialization in countries like France, and the persistence of older methods of artisanal production alongside new forms of mechanization. To understand the Industrial...more
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Correction To Heat Equation Discussion, Setup For Fourier Transform Derivation From Fourier Series, Results Of The Derivation: Fourier Transform And Inverse Fourier Transform, Definition Of The Fourier Transform (Analysis), Definition Of Fourier Inversion (Synthesis), Major Secret Of The Universe: Every Signal Has A Spectrum, Which Determines The Signal, Fourier Notation, Example: Rect Function, Example: Triangle Function
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This lecture picks off where the previous one left off, with a discussion of the legacies of John Brown. The most important thing about John Brown's raid, Professor Blight argues, was not the event itself, but the way Americans engaged with it after the fact. Next, Professor Blight discusses the election of 1860, a four-way battle won by the Republican candidate, Abraham Lincoln. In the wake of Lincoln's election, the seven states of the...more
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The most prominent chemist in the generation following Lavoisier was Berzelius in Sweden. Together with Gay-Lussac in Paris and Davy in London, he discovered new elements, and improved atomic weights and combustion analysis for organic compounds. Invention of electrolysis led not only to new elements but also to the theory of dualism, with elements being held together by electrostatic attraction. Wöhler's report on the synthesis of urea...more
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Recap: 'Difference Of Convex' Programming, Alternating Convex Optimization, Nonnegative Matrix Factorization, Comment: Nonconvex Methods, Conjugate Gradient Method, Three Classes Of Methods For Linear Equations, Symmetric Positive Definite Linear Systems, CG Overview, Solution And Error, Residual, Krylov Subspace, Properties Of Krylov Sequence, Cayley-Hamilton Theorem, Spectral Analysis Of Krylov Sequence
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February 11, 2009 lecture by Jefferson Tester for the Woods Energy Seminar (ENERGY301). In his talk "A Pathway for Widespread Utilization of Geothermal Energy--the Roles of Multi-scale Resource and Technology Research and Systems Analysis," Tester talks about the benefits and challenges of harnessing geothermal energy, and he asserts that it is a large resource that complements solar and wind energy and is both carbon free and scalable.
