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Circular Elastic Membrane

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This MATLAB GUI illustrates how the vibrating modes of a circular membrane evolve in time and interact with one another. The membrane is clamped at its boundary and its deflection from the horizontal, u, evolves according to the two-dimensional wave equation, utt = ∇2u.

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Diffusion at the Microscopic Level

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This MATLAB GUI simulates the random motion of M non-interacting particles on a grid. Each particle can only go up, down, left or right, with equal probability. All of the particles start their random walk from the origin, at the center of the box.

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Heat Equation on the Whole Line

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This MATLAB GUI plots the solution to the one-dimensional heat equation, ut = c2uxx, as a function of time and for "top hat" initial conditions.

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Julia Sets

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This MATLAB GUI iterates the quadratic map f(z) = z2+ c, where z and c are complex numbers. The (filled in) Julia set is the set of initial conditions z0 such that successive iterates z1 = f(z0), z2 = f(z1), ..., zn+1 = f(zn), ... remain bounded.

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Mass-Spring System

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This MATLAB GUI simulates the solution to the ordinary differential equation m y'' + c y' + k y = F(t), describing the response of a one-dimensional mass spring system with forcing function F(t) given by (i) a unit square wave or (ii) a Dirac delta function (e.g. "hammerblow'). Without loss of generality, m is set to 1.

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One-dimensional Heat Equation

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This MATLAB GUI illustrates the use of Fourier series to simulate the diffusion of heat in a domain of finite size. The quantity u evolves according to the heat equation, ut - uxx = 0, and may satisfy Dirichlet, Neumann, or mixed boundary conditions.

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Simple Plotter

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This MATLAB GUI provides a simple way of visualizing bifurcation diagrams by plotting functions that depend on a single control parameter. One of the functions could for instance be the right-hand side of the normal form of a standard codimension-one bifurcation, and the second function could be equal to zero.

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Rectangular Elastic Membrane

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This MATLAB GUI illustrates how the vibrating modes of a rectangular membrane evolve in time and interact with one another. The membrane is clamped at its boundary and its deflection from the horizontal, u, evolves according to the two-dimensional wave equation, utt = c2(uxx + uyy).

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Sea Shells

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This MATLAB GUI plots a variety of sea shells defined as parametric surfaces. An explanation of the significance of the various parameters may be downloaded from this web site.



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Sturm-Liouville Eigenfunctions

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This MATLAB GUI explores the orthogonality properties of several families of Sturm-Liouville eigenfunctions and emphasizes the geometric significance of the orthogonality relationship between two (different) eigenfunctions in the same family.

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Vibrating String

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This MATLAB GUI illustrates the use of Fourier series to simulate the dynamics of a vibrating string. The string is clamped at its end points and its deflection from the horizontal, u, evolves according to the wave equation, utt - uxx = 0.

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