discrete fourier transform
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Laplace transform of e^at.
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Solving a non-homogeneous differential equation using the Laplace Transform.
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Measure, fourier series, and fourier transforms
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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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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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Spatial Descriptions, Generalized Coordinates, Operational Coordinates, Rotation Matrix, Example - Rotation Matrix, Translations, Example - Homogeneous Transform, Operators, General Operators
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Professor Kleiner discusses the revolution in Roman architecture resulting from the widespread adoption of concrete in the late second and first centuries B.C. She contrasts what she calls innovative Roman architecture with the more traditional buildings already surveyed and documents a shift from the use of concrete for practical purposes to an exploration of its expressive possibilities. The lecture concludes with a discussion of the San...more
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This lecture is devoted to discussion of the wonderful Quantum world. Classical Mechanics, in spite of all of its impressive predictive power, fails to explain many microscopic behaviors. This led to the development of Quantum Mechanics, where electrons orbit nuclei in discrete energy levels, light can behave as a particle, and particles behave as waves. The location of microscopic particles can only be expressed in terms of probabilities....more
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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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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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Discrete source encoding
