systems of equations
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Review of Compilation Process of a Simple Program Into a .O File, Effect of Commenting Out a C Standard Library .H File on the Resulting Translation Unit, How Gcc Infers a Prototype When None Is Found and the .O File Remains the Same, How the Gcc Linker Is Able to Link Standard Library Files Without a #Include, The (Similar) Result When the .H File with Malloc's Prototype Is Not Included, How Commenting Out Assert.H Creates Different Resul...more
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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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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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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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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
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Genetics controls evolution. There are four major genetic systems, which are combinations of sexual/asexual and haploid/diploid. In all genetic systems, adaptive genetic change tends to start out slow, accelerate in the middle, and occur slowly at the end. Asexual haploids can change the fastest, while sexual diploids usually change the slowest. Gene frequencies in large populations only change if the population undergoes selection.
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This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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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
