Linear Algebra
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After discussing the statistical basis of the law of mass action, the lecture turns to developing a framework for understanding reaction rates. A potential energy surface that associates energy with polyatomic geometry can be realized physically for a linear, triatomic system, but it is more practical to use collective energies for starting material, transition state, and product, together with Eyring theory, to predict rates....more
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Stochastic Model Predictive Control, Causal State-Feedback Control, Stochastic Finite Horizon Control, 'Solution' Via Dynamic Programming, Independent Process Noise, Linear Quadratic Stochastic Control, Certainty Equivalent Model Predictive Control, Stochastic MPC: Sample Trajectory, Cost Histogram, Simple Lower Bound For Quadratic Stochastic Control, Branch And Bound Methods, Methods For Nonconvex Optimization Problems, Branch And Bound...more
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Recap: Subgradients, Subgradients And Sublevel Sets, Quasigradients, Optimality Conditions - Unconstrained, Example: Piecewise Linear Minimization, Optimality Conditions - Constrained, Directional Derivative And Subdifferential, Descent Directions, Subgradients And Distance To Sublevel Sets, Descent Directions And Optimality, Subgradient Method, Step Size Rules, Assumptions, Convergence Results, Aside: Example: Applying Subgradient Method...more
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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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Heat, conductivity, and thermal expansion are the discussed in this lecture. Both linear thermal expansion, leading to a need for expansion joints in railroad rails on hot days, and cubical thermal expansion, as occurs in a mercury thermometer, are covered in detail. The lectures ends with a focus on the cubical thermal expansion of water: the density of ice is about 8% lower than water, so ice cubes and icebergs float.
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The Concept of Underfitting and Overfitting, The Concept of Parametric Algorithms and Non-parametric Algorithms, Locally Weighted Regression, The Probabilistic Interpretation of Linear Regression, The motivation of Logistic Regression, Logistic Regression, Perceptron
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Optimal And Locally Optimal Points, Feasibility Problem, Convex Optimization Problem, Local And Global Optima, Optimality Criterion For Differentiable F0, Equivalent Convex Problems, Quasiconvex Optimization, Problem Families, Linear Program
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This lecture covers resistive forces such as air drag. It includes the viscous (linear in velocity) and pressure (quadratic in velocity) terms. Quantitative demonstrations with balloons and with ball bearings dropped in syrup are shown. He concludes with numerical calculations of air drag examples, also discussing the contribution of air drag to the quantitative experiments down earlier in the course with falling apples.
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Newton's Method (Cont.), Newton Step At Infeasible Points, Solving KKT Systems, Equality Constrained Analytic Centering, Complexity Per Iteration Of Three Methods Is Identical, Network Flow Optimization, Analytic Center Of Linear Matrix Inequality, Interior-Point Methods, Logarithmic Barrier
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Professor Sylvia Ceyer covers the molecular orbital theory, beginning with a discussion of some key topics including bonding orbitals, antibonding orbitals, electron configurations, and bond order. Using a wealth of examples to depict molecular orbitals (MOs) formed by the linear combination of atomic orbitals (LCAO), she concludes with heteronuclear diatomics.
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Guest Lecturer: Krasimir Kolarov, Trajectory Generation - Basic Problem, Cartesian Planning, Cubic Polynomial, Finding Via Point Velocities, Linear Interpolation, Higher Order Polynomials, Trajectory Planning with Obstacles
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August 3, 2006 presentation by Uwe Bergmann for the Stanford University Office of Science Outreach's Summer Science Lecture Series. Uwe Bergman, Physicist at the Stanford Linear Accelerator takes the viewer on a journey of a 1,000 year old parchment from its origin in the Mediterranean city of Constantinople to a particle accelerator in Menlo Park.
