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18 plays 0Mathematica Notebook -
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5 plays 0Legendre transform of non-convex bodies and shocks. -
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9 plays 0Recap of last time, Burgers equation and the Legendre transform -
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11 plays 0Back to Burger's equation -
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10 plays 0Legendre Transform -
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16 plays 0Laplace Asymptotics -
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8 plays 0Cole-Hopf Transform -
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7 plays 0The Burger's equation and the inviscid Burger's equation: Shocks and Fronts -
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8 plays 0Jacobi Identity -
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13 plays 0Method of Images Continued -
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13 plays 0What is up with that reflection formula? -
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15 plays 0Fundamental solution in one dimension on an interval. -
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21 plays 0Solutions to Heat Flow by eigenfunction expansion. -
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10 plays 0Proof of Maximum principle, Continuity of solution operator. -
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11 plays 0Statement of Parabolic Maximum principle -
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18 plays 0The initial-boundary value problem for the heat equation. -
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9 plays 0Root cellars and the skin effect -
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9 plays 0Sideways Heat equation - Implicit boundary condition and solution. -
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9 plays 0Sideways heat Equation: The root cellar problem. -
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9 plays 0Duhamel formula, for Heat equation -
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10 plays 0Backwards Heat Equation; Ill-Posedness -
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7 plays 0Higher dimensional solution -
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9 plays 0Properties of the solution to the one dimensional heat equation. -
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9 plays 0Solution of the one dimensional heat equation by fundamental solution -
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11 plays 0Continuum limit of the Random walk: One dimensional heat equation. -
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8 plays 0Laplace Asymptotics- Borderline recurrence in two dimensions, transience in three dimensions. -
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11 plays 0Random walk in two and three dimensions -
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14 plays 0Polya's theorem recurrence for one dimensional random walk. -
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16 plays 0Heat Equation, Random walk in one dimension. -
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13 plays 0Fourier transform of tempered distributions.
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Liberal Arts & Sciences
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- Center for East Asian and Pacific Studies
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- MCB Advising Program
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Lecture repository for Math 553 (Introduction to Partial Differential Equations) given in the Spring semester of 2020 at the University of Illinois.