Lecture 1: Overview of Topics, Course Mechanics.
September 6, 2011
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Lecture 2: Motivation, Examples of Infinite Dimensional and Distributed Systems.
September 8, 2011
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Lecture 3: Motivation, Examples of Infinite Dimensional and Distributed Systems (continued).
September 13, 2011
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Lecture 4: Examples of Solutions to Infinite Dimensional Systems.
September 15, 2011
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Lecture 5: Conversion of a Diffusion Equation to an Infinite Number/Continuum of Decoupled States; Dyadic Decomposition of an Operator.
September 20, 2011
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Lecture 6: Kernel Representation of Linear Operators/Systems.
September 22, 2011
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Lecture 7: Hilbert Space Adjoint of a Linear Operator.
September 27, 2011
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Lecture 8: Self-Adjoint Operators.
September 27, 2011
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Lecture 9: Spectral theory for compact normal operators; Schmidt Decomposition; Riesz-spectral operators.
October 4, 2011
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Lecture 10: Semigroup theory.
October 6, 2011
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Lecture 11: Examples of Strongly Continuous Semigroups; Hille-Yosida and Lumer-Phillips Theorems.
October 11, 2011
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Lecture 12: Waves, Beams, ...
October 13, 2011
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Lecture 13: ... and a bit of Fluids.
October 18, 2011
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Lecture 14: Non-Normal Dynamical Generators; An Example From Fluid Mechanics.
October 20, 2011
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Lecture 15: Systems with Inputs.
October 25, 2011
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Lecture 16: Controllability and Observability.
October 27, 2011
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Lecture 17: Spectral and Pseudo-Spectral Numerical Methods.
November 1, 2011
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Lecture 18: Pseudo-Spectral - Galerkin via Gaussian Quadrature; Matlab Differentiation Matrix Suite.
November 3, 2011
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Lecture 19: Introduction to Chebfun.
November 8, 2011
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Lecture 20: Frequency Responses and Input-Output Norms of Distributed Systems.
November 10, 2011
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Lecture 21: Input-Output Analysis in Fluid Mechanics.
November 15, 2011
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Lecture 22: Turbulence without Inertia; Exponential Stability.
November 17, 2011
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Lecture 23: Introduction to Optimal Control of Distributed Systems.
November 29, 2011
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Lecture 24: Design of Linear Quadratic Regulator for Spatially Invariant Systems.
December 1, 2011
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Lecture 25: Control of Vehicular Formations.
December 5, 2011
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Lecture 26: Vehicular Formation and Consensus Problems.
December 6, 2011
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Lecture 27: Coherence in Large-Scale Networks; Incidence Matrix of a Graph.
December 8, 2011
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Lecture 28: Optimal Control of Undirected Graphs; (A very brief) Introduction to Alternating Direction Method of Multipliers (ADMM).
December 9, 2011
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