Exponential Signals
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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....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...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,...more
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Prior to Malthus, population growth was seen as good for the power and wealth of a country. The rapid population growth of America was crucial in expelling England (via the Revolution) and France (via the Louisiana Purchase) from the US. But in fact, the numbers of the poor were growing in Europe in the 1700s. Malthus argued that poverty was due to an imbalance between people and resources; since population could rise very fast, it could...more
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Guest Lecturer, Setup of the Ice Cream Store Problem, with Customer, Cashier, Clerk, and Manager Threads, The Different Constraints on the Various Types of Threads, Writing the Main Function, Spawning the Various Threads, Handling the Manager-Clerk Interaction Using the Inspection Struct, Which Uses a Semaphore to Signal to the Manager That the Clerk Is Ready for Inspection, As Well as a Semaphore that Ensures that the Clerk Will Wait for...more
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We look at two settings with asymmetric information; one side of a game knows something that the other side does not. We should always interpret attempts to communicate or signal such information taking into account the incentives of the person doing the signaling. In the first setting, information is verifiable. Here, the failure explicitly to reveal information can be informative, and hence verifiable information tends to come out even...more
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Effect On Fourier Transform Of Shifting A Signal, Resulting Delay Formula (Shift Theorem), Effect Of Scaling The Time Signal, Stretch Theorem Formula/ Interpretation, Convolution In Context Of Fourier Transforms; Multiplying Two Signals In Frequency, Resulting Convolution Formula
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Review Of Main Properties Of The Shah Function, Setup For The Interpolation Problem, Bandwidth Assumption, Solving For Exact Interpolation For Bandlimited Signals, Periodizing The Signal By Convolution With The Shah Function, Solution Of The Interpolation Problem
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According to the rational expectations hypothesis, traders know the probabilities of future events, and value uncertain future payoffs by discounting their expected value at the riskless rate of interest. Under this hypothesis the best predictor of a firm's valuation in the future is its stock price today. In one famous test of this hypothesis, it was found that detailed weather forecasts could not be used to improve on contemporaneous...more
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Sexual selection is a component of natural selection in which mating success is traded for survival. Natural selection is not necessarily survival of the fittest, but reproduction of the fittest. Sexual dimorphism is a product of sexual selection. In intersexual selection, a sex chooses a mate. In intrasexual selection, individuals of one sex compete among themselves for access to mates. Often honest, costly signals are used to help the...more
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Newton's Method, Exponential Family, Bernoulli Example, Gaussian Example, General Linear Models (GLMs), Multinomial Example, Softmax Regression
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Professor Strang explains how the magic number e connects to ordinary things like the interest on a bank account. The graph of y = e^x has the special property that its slope equals its height (it goes up exponentially fast!). This is the great function of calculus.
