Constant Coefficients
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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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Methods (Truncated Newton Method), Convergence Versus Iterations, Convergence Versus Cumulative CG Steps, Truncated PCG Newton Method, Truncated Newton Interior-Point Methods, Network Rate Control, Dual Rate Control Problem, Primal-Dual Search Direction (BV Section 11.7), Truncated Netwon Primal-Dual Algorithm, Primal And Dual Objective Evolution, Relative Duality Gap Evolution, Relative Duality Gap Evolution (N = 10^6), L_1-Norm Methods...more
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Concerns about low fertility have been present in many countries for at least 100 years. A large population was considered essential to national power. But the issue is never simply a shortage of warm bodies: overall the world population has increased dramatically over this period and untold numbers would immigrate, if allowed. The issue is the number of the 'right sort' of people, defined as those having preferred national, religious,...more
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In this lecture, Professor Paul Fry turns his attention to the relationship between authorship and the psyche. Freud's meditations on the fundamental drives governing human behavior are read through the lens of literary critic Peter Brooks. The origins of Freud's work on the "pleasure principle" and his subsequent revision of it are charted, and the immediate and constant influence of Freudian thought on literary production is asserted....more
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Similarity between C++ & Java: - syntax - variable types - operators - control structures
Stanford / Computer Science
Similarity between C++ & Java: - syntax - variable types - operators - control structures, Looking at an Example C++ code: - comment, #include Statements, Global Declarations (constant), Declaring a Function Prototype, The main() Function, Decomposed Function Definition, Example Live Coding: To Calculate the Average, for loop - a while : Another Purpose of the Same Code, C++ User Defined Data Types: -enums -records, C++ Parameters...more
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Recap: Example: Minimum Cardinality Problem, Interpretation As Convex Relaxation, Interpretation Via Convex Envelope, Weighted And Asymmetric L_1 Heuristics, Regressor Selection, Sparse Signal Reconstruction, L_1-Norm Methods For Convex-Cardinality Problems Part II, Total Variation Reconstruction, Total Variation Reconstruction, TV Reconstruction, L_2 Reconstruction, Iterated Weighted L_1 Heuristic, Sparse Solution Of Linear Inequalities,...more
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Summary Of Previous Lecture (Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena), Fourier Coefficients; Discussion Of How General The Fourier Series Can Be (Examples Of Discontinuous Signals), Discontinuity And Its Impact On The Generality Of The Fourier Series, Infinite Sums To Represent More General Periodic Signals, Summary Of Convergence Issues, Convergence: Continuous Case, Smooth Case (Fourier Series...more
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Periodicity; How Sine And Cosine Can Be Used To Model More Complex Functions, Example Of Periodizing A Signal, Discussion Of How To Model Signals With Sinusoids, "One Period, Many Frequencies" Idea In Modeling Signals, Modeling A Signal As The Sum Of Modified Sinusoids (Formula), Complex Exponential Notation, Symmetry Property Of The Complex Coefficients In The Fourier Series, Discussion Of The Generality Of The Fourier Series...more
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DC Or Static Gain Matrix, Discretization With Piecewise Constant Inputs, Causality, Idea Of State, Change Of Coordinates, Z-Transform, Symmetric Matrices, Quadratic Forms, Matrix Nom, And SVD, Eigenvalues Of Symmetric Matrices, Interpretations Of Eigenvalues Of Symmetric Matrices, Example: RC Circuit
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This lecture is all about motion of projectiles (if air drag can be ignored). The objects experience a constant vertical acceleration due to the acceleration of gravity (see also Lecture 12). Professor Lewin reviews the equations for projectile motion, showing that the trajectory is a parabola. He continues with a demonstration that shows how to measure the initial speed of a projectile and how to reach maximum horizontal distance...more
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Professor Sylvia Ceyer explains the standard Gibbs free energy of formation and its relationship to thermodynamic stability. The Second Law of Thermodynamics is defined as it relates to controlling spontaneity with temperature. The lecture concludes by defining the thermodynamic equilibrium constant and the reaction quotient/direction of change in a chemical equilibrium.
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In this lecture Professor Sylvia Ceyer moves on from the wavelike properties of light, to the particle-like nature of light. To do so she covers the photoelectric effect in detail, discussing threshold frequency and kinetic energy vs. frequency. Planck's constant is discussed. The lectures concludes with a discussion of photon momentum and its relation to wavelength.
