Visualizations and computations in Mathematica for Partial Differential Equations SP19, Olin College. The Mathematica notebooks are based on Studios given in the course by Professor Aaron Hoffman.
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Studio1.nb: Basic functions such as triangular function, unit step function, standard Gaussian, Possion, Dirichlet, Heat, and Wave kernels; basic operations such as convolution.
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Studio2.nb: Wave equations visualzations with various initial conditions; characteristics of linear and nonlinear transport equations in the (t,x) plane with various initial conditions.
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Studio3.nb: Symbolic calculation of Lp norms of various functions. General convolution and frequency reponses of various functions and kernels.
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Studio5.nb: Numerical solutions and visualization of ODEs and PDEs with forcing
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Studio6.nb: Fourier series in one and two dimensions; symbolic calculation of Fourier series coefficients
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Studio7.nb: Piano wire modeling through the wave equation and Fourier series.
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Studio8.nb: Thermal modeling of the heat equation on a metal disk; numerically select the position of hammer that minimizes the energy of discordant overtunes of a piano wire.
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Studio9.nb: Poisson Kernel.
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Studio10.nb: Heat equation with boundary conditions on a wedge.
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E_M_Final.pdf: Applied PDE in Electricity and Magnetism; a summary of first nine chapter of D.J. Griffiths's Intro to Electrodynamics.
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E&M.nb: Applied PDE in Electricity and Magnetism through Reflection and Refraction and Absorption and Dispersion of Electromagnetic Waves; accompanies the E&M summary.