Category: Computer Science

Text and Exercise from “Boundary Value Problems Second Edition” by David L. Powers in Progress (c) Wednesday, April 17, 2024, James Pate Williams, Jr.

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Solution of the One-Dimensional Heat Equation for a Rod Using Finite Differences by James Pate Williams, Jr. Created on Wednesday April 3, 2024

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Undamped Mass-Spring Eigenvalue – Eigenvector Problem by James Pate Williams, Jr. (c) Monday April 1, 2024

We extend the results of the following website:

https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/3%3A_Systems_of_ODEs/3.6%3A_Second_order_systems_and_applications

The five masses in the problem have a maximum value of 8. The six springs have a maximum value of 4 for their Hooke’s coefficients. The first 5 by 5 matrix is the inverse mass matrix, the second matrix is the Hooke’s coefficient 5 by 5 matrix, the third 5 by 5 matrix is the product of the inverse mass matrix times the Hooke’s coefficient matrix. The final row vector is the eigenvalue vector.

A New and Some Old MP3s by James Pate Williams, Jr. Copyrighted on Easter Sunday, March 31, 2024

The first MP3 was created on Saturday, March 30,2024. It uses the former Cakewalk Digital Audio Workstation software SONAR Platinum. The software synthesizer utilized was Universal Audio Waterfall Hammond B3 Organ emulator with Lesley Type 147 amplifier and rotating speaker enclosure.

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The second MP3 was created on May 19,2009, using my Gibson EDS-1275 double neck SG guitar and one of the older Cakewalk DAWs. Unfortunately, my double neck guitar was stolen from my house in 2011.

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The final MP3 in this post uses my 2006 Gibson Les Paul SG Custom. The date on the MP3 is Thursday, February 15, 2018.

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The next MP3 is the same music as the first MP3 but using Universal Audio’s Mini Moog synthesizer with Fanfare preset.

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New 1d Integration Results (c) March 24, 2024, by James Pate Williams, Jr.

I tested NUMAL’s integration function versus homegrown trapezoidal rule and Simpson’s rule. The second and third algorithms were closed (included both endpoints). There exist higher order Newton-Cotes integration formulas. I did not test the Gauss-Legendre and/or Gauss-Laguerre integration method(s). The trapezoidal rule can be improved if the derivative of the integrand is known and is easily calculated.

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