analysis of linear systems
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Note: This course is being offered this summer by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. To...more
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Professor Kagan discusses in detail the argument of free will as proof for the existence of an immaterial soul. The argument consists of three premises: 1) We have free will. 2) Nothing subject to determinism has free will. 3) All purely physical systems are subject to determinism. The conclusion drawn from this is that humans are not a purely physical system; but Professor Kagan explains why this argument is not truly compelling. In addit...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.
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The course is an introduction to Dante and his cultural milieu through a critical reading of the Divine Comedy and selected minor works (Vita nuova, Convivio, De vulgari eloquentia, Epistle to Cangrande). An analysis of Dante's autobiography, the Vita nuova, establishes the poetic and political circumstances of the Comedy's composition. Readings of Inferno, Purgatory and Paradise seek to situate Dante's work within the intellectual and soc...more
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In discussions of the Schrödinger equation thus far, the systems described were either one-dimensional or involved a single electron. After discussing how increased nuclear charge affects the energies of one-electron atoms and then discussing hybridization, this lecture finally addresses the simple fact that multi-electron systems cannot be properly described in terms of one-electron orbitals.
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The simple harmonic oscillations (SHO) of suspended solid bodies are related to their geometry. The torsional pendulum oscillates in the horizontal plane; the SHO does NOT depend on the small angle approximation. In this lecture Professor Lewin discusses the SHO equation of motion for a rigid body pendulum, for a liquid sloshing in a U-shaped tube, and for a torsional pendulum.
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Kernels, Mercer's Theorem, Non-linear Decision Boundaries and Soft Margin SVM, Coordinate Ascent Algorithm, The Sequential Minimization Optimization (SMO) Algorithm, Applications of SVM
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Complexity; log, linear, quadratic, exponential algorithms
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An Application of Supervised Learning - Autonomous Deriving, ALVINN, Linear Regression, Gradient Descent, Batch Gradient Descent, Stochastic Gradient Descent (Incremental Descent), Matrix Derivative Notation for Deriving Normal Equations, Derivation of Normal Equations
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In this introductory lecture, Professor Lewin discuses basic units, dimensions, measurements and associated uncertainties, dimensional analysis, and scaling arguments. Further, he explains why a measurement is meaningless without knowledge of its uncertainty, using data collected by Galileo Galilei as an example. He begins to dive into dimensional analysis, reasoning that the time from an object to fall from a certain height is independen...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 coloni...more
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The rise of absolutism in Europe must be understood in the context of insecurity attending the religious wars of the first half of the seventeenth century, and the Thirty Years' War in particular. Faced with the unprecedented brutality and devastation of these conflicts, European nobles and landowners were increasingly willing to surrender their independence to the authority of a single, all-powerful monarch in return for guaranteed protec...more
