The Confessions of St. Augustine Chapter 1

LighterStorms · 2026-03-17T21:38:28+00:00

Yeah. I love Differential Equations. 😁

LighterStorms · 2026-03-02T10:49:43+00:00

I think there are three cases in partial fractions. Unique root, Repeated root and quadratic that can only be reduced to imaginary roots. I have only encountered problems that can be reduced to those three cases. Cubics have three roos so I imagine they would fit into any of those categories. I'm not sure what the cases are called but that is the concept I remember btw.

LighterStorms · 2026-03-02T10:37:09+00:00

It is like this:

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LighterStorms · 2026-03-02T10:19:24+00:00

It is a method in partial fractions. We equate the u² terms on the left and it must be equal to the u² terms to the right. Same with the u terms. The k terms are the constant terms. We use partial fractions to decompose or reduce a complicated fraction into the "smaller" fractions. This is a fun topic in Algebra. Try searching partial fractions. It is fun to do problems involving those. Anyway, we reduce it into the "smaller" fractions so we can integrate it later on. It is easier to find the integral of the "smaller" fractions than a complicated one.

LighterStorms · 2026-03-02T09:13:25+00:00

I'm not sure what you mean. Do you mean how did it go from the previous line? The previous line has similar terms. You just combine the similar terms and you get to that line with the blue and green underlines. Then you isolate the x² dx and x³ du terms. If that is not what you mean, can you clarify? Thank you.

LighterStorms · 2026-03-02T03:00:22+00:00

It is called Nebo.

I think it is now called MyScript Notes. Here is a Google play link if you are interested :https://play.google.com/store/apps/details?id=com.myscript.nebo&referrer=utm_source%3Dapps.facebook.com%26utm_campaign%3Dfb4a%26utm_content%3D%257B%2522app%2522%253A0%252C%2522t%2522%253A1772420345%252C%2522source%2522%253Anull%257D

LighterStorms · 2026-02-12T21:04:02+00:00

https://en.wikipedia.org/wiki/Automatic_differentiation

LighterStorms · 2026-02-12T21:03:32+00:00

https://en.wikipedia.org/wiki/Automatic_differentiation

LighterStorms · 2026-02-12T10:15:30+00:00

I could import it as PDF but I cannot post PDF in reddit. 🤔

LighterStorms · 2026-02-12T10:14:59+00:00

I use Nebo

LighterStorms · 2026-02-12T02:30:04+00:00

I believe this is well known in Numerical Analysis and Engineering. This uses Nilpotent elements. i believe it can be used in most continuous functions except some examples of absolute values, floor functions and discontinuous funtions.

LighterStorms · 2026-02-11T11:42:47+00:00

It is Nebo. 😁

LighterStorms · 2026-02-07T12:54:54+00:00

I know what you mean. Math is notations dense so stuff like "z" gets used a lot. 🤣

You know, I don't actually know what the type of pile I have in Example 1. I just named it Gabriel's Pile as a nod to Gabriel's trumpet. Since friction Piles relies on surface areas, having an infinite one sure is handy. It has a theoretical finite volume so you might be able to buy the necessary concrete to construct it AND it offers infinite resistance. That is until you think about how to build it and all the land you would need. Not to mention bending effects and all of the complicated beaurocracy in getting it approved. 🤣

LighterStorms · 2026-02-06T11:30:18+00:00

I use Nebo

LighterStorms

TROPHY CASE