Systems Of Equations
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Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix
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State-action Rewards, Finite Horizon MDPs, The Concept of Dynamical Systems, Examples of Dynamical Models, Linear Quadratic Regulation (LQR), Linearizing a Non-Linear Model, Computing Rewards, Riccati Equation
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LU Factorization (Cont.), Sparse LU Factorization, Cholesky Factorization, Sparse Cholesky Factorization, LDLT Factorization, Equations With Structured Sub-Blocks, Dominant Terms In Flop Count, Structured Matrix Plus Low Rank Term
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Jeff Raikes, group vice president of Productivity and Business Services (PBS) at Microsoft Corporation, explains his own background and how being open to opportunities helped him become the only undergraduate from the Engineering Economic Systems department at Stanford.  Plans change as opportunities arise, he says. He also recommends entrepreneurs look for a job they love.
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The simple harmonic oscillations (SHO) of suspended solid bodies are related to their geometry. The torsional pendulum oscillates in the horizontal plane; the SHO does NOT depend on the small angle approximation. In this lecture Professor Lewin discusses the SHO equation of motion for a rigid body pendulum, for a liquid sloshing in a U-shaped tube, and for a torsional pendulum.
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Markov Chain (Example), Diagonalization, Distinct Eigenvalues, Digaonalization And Left Eigenvectors, Modal Form, Diagonalization Examples, Stability Of Discrete-Time Systems, Jordan Canonical Form, Generalized Eigenvectors
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November 30, 2007 lecture by Ted Selker for the Stanford University Human-Computer Interaction Seminar (CS 547). This talk demonstrates that Artificial intelligence can competently improve human interaction with systems and even each other in a myriad of natural scenarios.
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Least-Norm Solution, Least-Norm Solution Via QR Factorization, Derivation Via Langrange Multipliers, Example: Transferring Mass Unit Distance, Relation To Regularized Least-Squares, General Norm Minimization With Equality Constraints, Autonomous Linear Dynamical Systems, Block Diagram
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Smith talks about how New Ventures aims to create systems that are K-12 to provide a coherent experience to children. Incubation is important. New Schools buys run down buildings and turns them into successful schools. They do everything from recruitment to management to building, she adds.
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Manipulator Control, PD Control Stability, Task Oriented Control, Task Oriented Equations of Motion, Operational Space Dynamics, Example, Nonlinear Dynamic Decoupling, Trajectory Tracking
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Professor Shankar introduces the course and answers student questions about the material and the requirements. He gives an overview of Newtonian mechanics and explains its two components: kinematics and dynamics. He then reviews basic concepts in calculus through two key equations: x0 + v0t + ½ at2 and v2 = v02+ 2 a (x-x0), tracing the fate of a particle in one dimension along the x-axis.
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Lagrangian, Lagrange Dual Function, Least-Norm Solution Of Linear Equations, Standard Form LP, Two-Way Partitioning, Dual Problem, Weak And Strong Duality, Slater's Constraint Qualification, Inequality Form LP, Quadratic Program, Complementary Slackness
