dimensional analysis
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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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Using vectors to solve 2 dimensional projectile motion problems.
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Another example of a 2-dimensional projectile motion problem.
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We finish the 2-dimensional momentum problem.
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More on 2 dimensional projectile motion.
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After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analog...more
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The Factor Analysis Model,0 EM for Factor Analysis, Principal Component Analysis (PCA), PCA as a Dimensionality Reduction Algorithm, Applications of PCA, Face Recognition by Using PCA
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Algorithm Analysis, Evaluating the Performance, Analysis of Codes: Statement Counts, Another Example (Statement Count Contd.), Comparing Algorithm, Big-O Notation, Big-O to Predict the Time of Execution, Best/Worst/Average Case, Analysis of Recursive Algorithms, Another Example : Towers of Hanoi, A Tabulation for Different Algorithms, Growth Patterns, Application of Algorithm Analysis to Sorting, Selection Sort, Selection Sort Code
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A Wrap Up of Multi-dimensional Arrays, The ArrayList Way, Pros and Cons : ArrayList vs. Array, Debugging, Approaches to Debugging, The Debugger in Eclipse
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Multi-dimensional Arrays, An ArrayList, The Template Class, Methods in the ArrayList Class, An Example Program Using ArrayList, ArrayLists Hold Objects, An Example Program with an ArrayList of Glabels, The GrayImage Example Program
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The visual system has developed to allow us to navigate in a complex and dangerous world in order to find food and to avoid danger. This survival system works by building a complex three-dimensional model based on two-dimensional data from the retina. This model is tested against "reality" and checked with information from other senses and updated if needed. The brain suppresses the complexity of this processing and we believe that visi...more
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Mixture of Gaussian, Mixture of Naive Bayes - Text clustering (EM Application), Factor Analysis, Restrictions on a Covariance Matrix, The Factor Analysis Model, EM for Factor Analysis
