periodic solutions
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Statistics 110 (Probability), which has been taught at Harvard University by Joe Blitzstein (Professor of the Practice, Harvard Statistics Department) each year since 2006. Lecture videos, review materials, and over 250 practice problems with detailed solutions are provided. This course is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are use...more
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, ...more
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Stoichiometry of chemical reactions, quantum mechanical description of atoms, the elements and periodic table, chemical bonding, real and ideal gases, thermochemistry, introduction to thermodynamics and equilibrium, acid-base and solubility equilibria, introduction to oxidation-reduction reactions.
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especial...more
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A special event to mark the publication of Professor Barrow's new book, 'The Book of Universes'. This is a book about universes, a story that revolves around a single unusual and unappreciated fact: that Einstein’s famous theory of relativity describe universes – entire universes. Not many solutions of Einstein’s tantalizing universe equations have ever been found, but those that have are all very remarkable. Some of them describe universe...more
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In the first or second year of his medical residency training in the US in 1978, Palmaz went to an early meeting of the Society of Cardiovascular Intervention and Radiology in New Orleans. The keynote speaker was a young professor from Germany, Andreas Grunzig, who was coming to the states to report on his early experience with balloon angioplasty. Grunzig was charasmatic and intelligent, and explained balloon angioplasty so clearly--benef...more
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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 titratio...more
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Tarun Khanna, Professor at Harvard Business School, highlights the ability of entrepreneurs to provide solutions to social problems by telling the story of a cardiac hospital in India. Khanna points out that the founder, a cardiac surgeon and entrepreneur, has been able to achieve incredible results unmatched by private or public institutions around the world by rethinking the scale on which healthcare is delivered. Khanna emphasizes that ...more
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After a mock trial session to whittle down the most critical causes from an applicant pool of 10,000, Google.org chose just five areas of concentration: renewable energy, plug-in vehicles, prevention of pandemics, famines, and floods, public services for the poor, and job creation. And the organization's Executive Director, Larry Brilliant, offers this overview of these pressing global issues, and pinpoints Google's resources dedicated tow...more
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Life history covers three main classes of traits in organisms: age and size at maturity, number and size of offspring, and lifespan and reproductive investment. Organisms must make tradeoffs among these traits that typically cause them to come to evolutionary equilibrium at intermediate values. Life history traits are evolutionary solutions to the ecological problems of the risk of mortality and the acquisition of food, and they are expres...more
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Equity Risk Premia and Bond default spreads Equity Risk Premia and Real Estate Cap Rates Implied premia for emerging markets Betas - The problem with regression betas - Solutions
