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mathematica

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Thesis for the Computational Science Master's program at Central Washington University. 3D extension of an analog of cosmological particle creation in a Friedmann-Robertson-Walker universe by numerically simulating a Bose-Einstein condensate with a time-dependent scattering length.

  • UpdatedJun 11, 2025
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In this manuscript, we show new binomial identities in iterated rascal triangles, revealing a connection between the Vandermonde convolution and iterated rascal numbers. We also present Vandermonde-like binomial identities. Furthermore, we establish a relation between iterated rascal triangle and (1,q)-binomial coefficients.

  • UpdatedJan 14, 2025
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The power rule for derivatives, typically proven through the limit definition of derivative in conjunction with the Binomial theorem. In this manuscript we present an alternative approach to proving the power rule, by utilizing a certain polynomial identity, such that expresses the function's growth.

  • UpdatedJun 16, 2025
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