To check my digits perhaps use and trust the web application:
The First 5000 Digits of the Transcendental Number Pi by James Pate Williams, Jr.
Category: Numerical Analysis
Ground State Energy of the Helium Atom and Lithium Atom by James Pate Williams, Jr.
Ground State Energy of the Helium Atom by James Pate Williams, Jr.
Solving Four Elliptic Partial Differential Equations Using the Finite Element Method by James Pate Williams, Jr.
The equations I solve in this blog entry are from a thesis that uses artificial neural networks to solve partial differential equations:
https://dukespace.lib.duke.edu/dspace/handle/10161/8197
Here are the equations snipped from the thesis:
Alpha is defined as 0.5 * n. In our case n = 1, 2, 3, 4.
The solutions for the four cases above are graphed using Microsoft Mathematics:
The Microsoft Mathematics Application Window is illustrated below:
Min-Max Polynomial Curve Fitting by James Pate Williams, Jr., BA, BS, MSwE, PhD
On Sunday, August 28, 2016, 3:57:53 PM I created a C# program to fit a given curve to a polynomial of a specified degree and number of points. Here are ten experiments with a continuous function to be discretely fitted by a polynomial.
Power Series – MacLaurin Series by James Pate Williams, Jr., BA, BS, MSwE, PhD
Baseball Ballistics by James Pate Williams, Jr., BS, BS, MSwE, PhD
There are analytic equations that are applicable to the trajectory of a batted or thrown baseball:
Click to access 04-LAJPE-782_Chudinov.pdf
I created a C# application to test the preceding equations against numerical methods of calculating the trajectory of a baseball. The baseball has an initial velocity of 90 miles per hour and an angle of inclination of 20 degrees. The classical model certainly overestimates the trajectory.
System of Ordinary Differential Equations Model of the United States COVID-19 Pandemic by James Pate Williams, Jr., BA, BS, MSWE, PHD
Siacci’s Method by James Pate Williams, Jr. BA, BS, MSwE, PhD
Siacci’s Method Chapter 5 and Appendix A of “Exterior Ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann of the United States Naval Academy. This is an approximate technique for solving exterior ballistics trajectories with between 12 to 15 degrees of elevation. The artillery is the 16 inch / 50 caliber rifled guns of the Iowa class of fast battleships (BB-61 USS Iowa, BB-62 USS New Jersey, BB-63 USS Missouri, and BB-64 USS Wisconsin).
From “Exterior Ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann by James Pate Williams, Jr., BA, BS, MSwE, PhD
Numerical Explorations 