#Laplace Formulae

[arttsuka]

is it like- class work sheet or something like that?

Yeah formula sheet, makes sense

[the-necromancer-wife]

"I could explain more about the Laplace Demon concept if you, dear readers, are interested but that would be for another occasion. Another essay hehe."

Pleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleasepleaseplease 🛐

Explaining Laplace's Demon tehory in the context of 14dwy.

Thank you so much for giving me an excuse to talk about this dear anon!

In this post i'll elaborate further about something i said in the end of this super long post. As always TW for 14dwy spoilers!

(Joke's on you, sir, i DID come here for the tales of old)

And this tale in specific is really old. Around two hundred years old to be specific. In 1814 a man known by the name Pierre-Simon de Laplace wrote an essay about a deterministic concept known later as the "Laplace's demon" (although he already seemed to be exploring this concept since 1773)

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past could be present before its eyes.

(Pierre Simon Laplace, Philosophical Essay on Probabilities.)

But what does this all mean? Well basically this man spoke about a hypothetical "intelligence" (he didn't precisely used the word "demon") that, knowing the precise location of every particle in the universe and where they were headed, they would be able to guess the past and future values for any given time. In other words, we would be referring to an almighty hypothetical "thing" able to see the past and future of every single thing in the universe.

Of course this is all a model, a theory, an exploration on what would happen if something like this existed in the first place. After all, it was all a philosophical essay in the first place, wasn't it?

"Une intelligence ... Rien ne serait incertain pour elle, et l'avenir, comme le passé, serait présent à ses yeux."

Of course, Mr. Laplace wasn't the only one to explore the idea of an almighty intelligence since other philosophers like Condorcet, Holbach and Diderot also wrote about it.

Now there are several theories (some more modern than others) to explain why an intelligence of this nature will never be possible to exist but there is one that might ring a bell for some people "The Chaos Theory"

Or as some might know it: The butterfly effect.

This theory basically poses that minor variations between the starting conditions of two systems can result in major differences. That's why you say that "A butterfly flying in certain direction today can lead to huge catastrophes tomorrow" it's not something (so) literal but it is useful to illustrate how small can be the variation and how huge can be the result. Of course the change doesn't have to be huge. It can be a minor change, but a change nonetheless.

Btw chaos theory is applicable when knowledge of the system is imperfect, whereas Laplace's demon assumes perfect knowledge of the system, therefore the variability leading to chaos in chaos theory and non-variability in the knowledge of the world Laplace's demon holds are noncomparable.

But, What does this all has to do with 14dwy?

Glad you ask. Actually a lot.

Starting off with the idea of how perfect is this game integrating even its genre (Visual Novel) to the theory. I believe there is no bigger example of the butterfly efect than a Visual Novel, where choosing (or not) certain options can lead to certain results (big or small). Very much like the butterfly effect. And funnily enough, it's us, the player, the embodiment of this umpredictability, since we are the ones that make the choices in the game. We are the antagonists of a hypothetical Laplace's Demon. We are it's antonym. We are an angel. The idea of a change that the system cannot predict. Of course this is questionable. Because as much as we have certain "freedom" we still need to abide by the choices that the very game gives to us.

This takes us back to the question of who is the entity that speaks to us in this cryptic messages on day four? Who is this (allegedly) Laplace's Demon? and what are my personal arguments on why i don't think it's [REDACTED].

Let's start by breaking down the messages. I have them all decoded in my previous post along with a really easy (i hope so) explanation on how the cipher works.

"...ATTEMPTING TO REWRITE WHAT HAS ALREADY BEEN ORDAINED SINCE THE BEGINNING"

Here, the entity mentions the certainty of the past, but not the certainty of the future.

"...ATTEMPTING TO DIG UP THE ROOTS OF FATE AS THOUGH IT WERE A WEED AND PLANTING YOUR OWN CORRUPT SEEDLING IN ITS PLACE"

Here, the entity presumably refers to the idea of our (very limited) free will and how we're pushing the limits of the system (in this case by attempting to keep advancing on a route that supposedly leads nowhere else). To make this more clear, this entity speaks to us when we load the save file multiple times trying to keep advancing down that path when the course of action contemplated is that we should just stop and load another save file. We're persistent creatures, after all.

"PERHAPS WE ARE THE SAME, THEN"

Of course fucking ✨not✨

"I TOO FIND ENJOYMENT IN DISRUPTING THE VINES OF KISMET AND WATCHING HIM STRUGGLE"

Now i swear i never heard the word "kismet" before this day. But it seems to be some sort of archaic synonim of the word "fate". Although according to Cambridge Dictionary it is actually "A force that (some people) think controls what happens in the future, and is outside human control"

Also, this entity seems to be having its fun with Ren/REDACTED's struggles. It doesn't really see our unpredictability (yet) as a threat.

"TWAS I WHO GAVE HIM HIS GIFT, AS I DID WITH OTHERS..."

AND THIS

This right here boy oh boy.

I gave him his gift: A rant about human deities through the holy act of programming.

(As pretentious as this title is, please hear me out)

There's a really interesting article named Embracing Λόγος: Programming as Imitation of the Divine that basically says:

The programmer must begin by defining things – material or conceptual. “We are unable to reason or communicate effectively if we do not first make the effort to know what each thing is.” (Rayside, Campbell) By considering the ontological questions of the things in our world, in order to represent them accurately (and therefore ethically) in our programs, the programmer enters into the philosophical praxis. Next, the programmer adds layers of identity and logic on top of their ontological discovery, continuing in the praxis.

But the programmer takes it a step further – the outcome of their investigation is not only their immaterial thought but, in executing the program, the manifestation of their philosophical endeavor into material reality. The program choreographs trillions of elementary charges through a crystalline maze, harnessing the virtually infinite charge of the Earth, incinerating the remains of starlight-fueled ancient beings in order to realize the reasoning of its programmer. Here the affair enters into the realm of Ethics.

“The programmer is attempting to solve a practical problem by instructing a computer to act in a particular fashion. This requires moving from the indicative to the imperative: from can or may to should. For a philosopher in the tradition, this move from the indicative to the imperative is the domain of moral science.” (Rayside, Campbell) Any actions taken by the program are the direct ethical responsibility of the programmer.

Furthermore, the programmer, as the source of reason and will driving a program, manifesting it into existence, becomes in that instant the λόγος σπερματικός (“logos spermatikos”) incarnate. The programmer’s reason, tapped into the divine Reason (λόγος), is generated into existence in the Universe and commands reasonable actions of inanimate matter.

Basically the programmer goes through each and every stage a deity would go through when creating the universe.

AND GUESS WHO IS A PROGRAMMER IN 14DWY???

(Ren/REDACTED in case you don't know hehe)

When the entity says "I gave him his gift" i believe this is exactly what he is referring to. While a Laplace's Demon knows every particle in the physical systems (and assumes it's knowledge of said system is perfect), a programmer works with Operative Systems (Windows, Linux, Ubuntu).

As for us, the angel, the antagonist of the demon of Laplace, we are the chaos theory, the one that conceives the knowledge of the system as imperfect.

Btw the person manipulating some choices in certain moments? Totally Ren/REDACTED. As they have the power of messing with the game and are totally self-aware of this being a visual novel.

But who gave Ren/REDACTED this power? Was Ren/REDACTED so skillful that they were able to defy the laws of worldbuilding? Picture this: the equivalent would be a programmer in the real world so skillful that they become able to defy the reality itself.

I believe the responsible is this "all knowing entity" since it just said it itself "It was I who gave him his gift". After all he is, and i quote, "THE PAST, PRESENT, AND FUTURE, COMBINED INTO ONE" really ominous shit.

There are obvious gaps in this theory but it's the best i can do with the limited knowledge i have. I am not a physicist so i can't really dwell in formulas and numbers as much as i would. Maybe i'll interview a professor in college in the future but for now i hope this is enough.

[acesw]

On Hofmann's death and Picrasma Poisoning

Picrasma is one of the key components in the candies and potions that essentially maintains or even boosts the energy of an arcanist. While it doesn't do anything to maintain one's control over their arcane skills, the plant does is able to maintain the activity of the cell colony.

However, while the picrasma plant itself is not poisonous, the picrasma solutions are not safe for humans to consume in all senses. Medicine Pocket has additionally noted that whatever is safe for humans to consume isn't effective on arcanists, so there's no possibility that picrasma can be used as an energy-boosting drug anytime soon.

"Experiment Record," The Clashing Tides — 06-19

When it comes to applying Laplace's solution to humans, they'll develop irritation and sores in the skin. This means it isn't lethal.

But if the components of the formula is changed, then the same cannot be said. In Forget Me Not's potion, it absolutely enhances the abilities of an arcanist, even making them more emotionally reactive to the environment around them. However, this potion becomes lethal to both pureblood and mixed humans.

War And Peace — 06-20

Which makes sense, the picrasma extract makes up 50% of the potion. This leads arcanists to have a huge adrenaline rush and become susceptible to emotional anguish. Meanwhile, humans would begin to feel their body collapse.

War And Peace — 06-20

The potion is designed to make death painfully slow. In Hofmann's case, it makes it all the more painful due to the fact that she is of mixed blood. It forcefully activated the weaker and more dormant parts of her vessels, making it difficult to breathe and even move.

"Not the Last," Finished Page — 06-22

It creates a grotesque pattern of lethal veins that spread from the heart. In other words, her own mind and body became immensely overwhelmed in all senses, and she would've been in horrible agony even if she lived. It makes her death from the gunshot wound all the more merciful in comparison.

[the-blossica-fan]

Side note, I ended up stumbling upon Lucy/Simone twitter, and I gotta be honest I see the vision!

Like, at first, you think it's your typical struggling assistant/eccentric boss based on the trailer. But then you actually *get* to the chapter, and it turns out nah nah nah. Simone is extremely used to working under Lucy and, in fact, understands how she thinks very well. She knows exactly what to say to keep Lucy motivated and on task during times of high stress and knows her limits. Simone also never forgets that Lucy isn't "human," so there are things that she might not understand, but she'd appreciate knowing the answer to.

Lucy, vice versa, trusts Simone implicitly. She tells Simone her plans and knows that even if Simone doesn't "get it," she'll do everything in her power to see it done. She also doesn't question Simone's insights or dismiss her questions, showing a level of respect befitting towards an assistant. Simone is Lucy's subordinate, but (probably because she's an Awakened) she doesn't treat Simone as actually beneath her.

Which is why I think that even if Lucy is "on vacation" in Vertin's suitcase, Simone is there too. We never saw Simone lose her position as Lucy's assistant, so clearly, that's still her job. When asked, Simone clarifies that on all official documentation, she is listed as Lucy's assistant, not the director of Laplace's assistant. So until Lucy herself deems her presence unnecessary, by her side, she will stay. Lucy nods and will immediately explain the benefits of keeping Simone with her and that Vertin is free to request her assistance in administrative duties if need be. Vertin wisely realizes their relationship is like Madame Z and Toothfairy's and wishes them a pleasant time in the suitcase and to let her or Sonnetto know if there is anything they need before leaving, making a mental note that despite her words Lucy just seems happier having Simone at her side.

YES

YES YES YES YOU SEE IT TOO

Lucy x Simone is an interesting ship because despite being Boss x Secretary, it's a break in the usual formula, and it's also not just quirky boss and tired secretary either, they both understand each other and know how to keep the other going.

It's such a good ship and I love it so much I need people to talk to it about me as passionately as we do about every other ship. I think it's pretty underrated.

Lucy is certainly non human, and it shows a lot in everything she does, yet Simone is never truly bothered by it. She doesn't question Lucy because she knows what she's doing, so much different from everyone around her who views her as someone who doesn't understand humanity.

It's just so good man, I think most R1999 ships break an already established formula in the most interesting way and it should be pointed out more, it makes them more compelling and endearing even if you don't ship it.

That being said

HELL YEAH WE GOT A NEW LUCY X SIMONE ENJOYER GOD IS GOOD

[scotianostra]

The Scottish Polymath Mary Somerville died on November 28th 1872 in Naples.

Today Somerville’s name lives on in an Oxford college, but her wider legacy is largely forgotten. She is the face of the Royal Bank of Scotland’s £10 banknote – the first non-royal woman to be honoured in this way.

Born in Mary Fairfax, Jedburgh on 26th December, 1790, Somerville grew up in the Fife seaside town of Burntisland. She was fascinated by the natural world from the start, collecting shells and fossils, and observing birds and sea creatures.

When her father returned from the sea, he discovered 8- or 9-year-old Mary could neither read nor do simple sums. He sent her to an elite boarding school, across the Firth of Forth, Miss Primrose's School in Musselburgh.

Miss Primrose was not a good experience for Mary and she was sent home in just a year. She began to educate herself, taking music and painting lessons, instructions in handwriting and arithmetic. She learned to read French, Latin, and Greek largely on her own. At age 15, Mary noticed some algebraic formulas used as decoration in a fashion magazine, and on her own she began to study algebra to make sense of them. She surreptitiously obtained a copy of Euclid's "Elements of Geometry" over her parents' opposition.

Four years after marrying, Mary Somerville and her family moved to London. Their social circle included the leading scientific and literary lights of the day, including Ada Bryon and her mother Maria Edgeworth, George Airy, John and William Herschel, George Peacock, and Charles Babbage. Mary and William had three daughters and a son who died in infancy. They also traveled extensively in Europe.

In 1826, Somerville began publishing papers on scientific subjects based on her own research. After 1831, she began writing about the ideas and work of other scientists as well. One book, "The Connection of the Physical Sciences," contained discussion of a hypothetical planet that might be affecting the orbit of Uranus. That prompted John Couch Adams to search for the planet Neptune, for which is he is credited as a co-discoverer.

Mary Somerville's translation and expansion of Pierre Laplace's "Celestial Mechanics" in 1831 won her acclaim and success: that same year, British prime minister Robert Peel awarded her a civil pension of 200 pounds annually. In 1833, Somerville and Caroline Herschel were named honorary members of the Royal Astronomical Society, the first time women had earned that recognition. Prime Minister Melbourne increased her salary to 300 pounds in 1837. William Somerville's health deteriorated and in 1838 the couple moved to Naples, Italy. She stayed there most of the remainder of her life, working and publishing.

In 1848, Mary Somerville published "Physical Geography," a book used for 50 years in schools and universities; although at the same time, it attracted a sermon against it in York Cathedral.

William Somerville died in 1860. In 1869, Mary Somerville published yet another major work, was awarded a gold medal from the Royal Geographical Society, and was elected to the American Philosophical Society.

By 1871, Mary Somerville had outlived her husbands, a daughter, and all of her sons: she wrote, "Few of my early friends now remain—I am nearly left alone." Mary Somerville died in Naples on November 29, 1872, just before turning 92. She had been working on another mathematical article at the time and regularly read about higher algebra and solved problems each day.

Her daughter published "Personal Recollections of Mary Somerville" the next year, parts of a work which Mary Somerville had completed most of before her death.

[phaedinphaedout]

I figured this out last night and I feel like it’s a very obvious fact that was glaring me in the face in hindsight but bc I haven’t seen anyone explicitly mention this I have decided to Break My Silence and hopefully string together a coherent sentence X and MP had me confused for a bit bc they’re both researchers…..scientists……in Laplace Institute (idc for the name) and ik they’re in different departments or w/e but for some reason X’s field of research is so much clearer than MP’s in comparison Turns out I was just not playing connect the dots hard enough anyway check this out

First thought for me here was: oh, MP made the Picrasma Candy?? Cool, v cool Second thought: what does being a masochist have to do with researching…..

I scroll back up on the wiki. I read these descriptions. Suddenly I understand

So MP uses their own body for experiments. Ohhh, ok. That explains why all their voicelines and other things are about stabbing themself with a syringe or asking you [Vertin] to write stuff down or smth along those lines……it’s bc MP [is] the test subject, MP doesn’t need any other bitches bc they ARE that bitch……..

This is in comparison to X’s voicelines, where he asks you to participate in experiments more often than MP does

And from what we can infer from some of MP’s voicelines, some of the experiments they conduct on themselves (likely done in Wilderness/Vertin’s suitcase) - probably experiments where it’s more life-risking/dangerous for them (hey dude, in what situation would you be counting your ribs??) - are experiments they’re not allowed to conduct in Laplace Research Institute (which gives them a viable reason to join Vertin’s group). The experiments MP normally conducts should all be related to general physical testing, if you consider the mentions of a training ground, frisbees, etc, and that’s probably how they managed to develop Picrasma Candy as well (through rigorous testing until they developed the current best formula for the candy)

[xenodile]

Okay, the Matis squad are all named for famous theories in mathematics and physics.

Maxwell, the mad scientist hellbent on squeezing more energy out of her generator than should be physically possible is named for Maxwell's Demon, a thought experiment suggesting that skillful and deliberate manipulation of particles could reverse entropy and produce infinite energy.

Drake, the egotist wannabe supervillain who is obsessed with becoming the single most well known and popular person in the world despite already being beloved by the entire population of Ark, is named after The Drake Equation, a theoretical formula for estimating the possible number of intelligent civilizations in the Milky Way galaxy.

And Laplace, the arrogant superhero that believes she should be everywhere, do everything, and cannot fail, is named for Laplace's Superman, a hypothetical super intellect that achieves omnipotence by knowing the positions of every atom in the universe.

[wayti-blog]

“We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.”

― Pierre Simon de Laplace (1749 – 1827), French scholar and polymath whose work was important to the developmentof engineering, mathematics, statistics, physics, astronomy, and philosophy

[locus-assignments-blogs]

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[quinn-fucks-shit-up]

the most irritating thing about doing engineering is that as soon as you start understanding those complicated diagrams and formula they start to look 1000% lamer and less cool

bitches will show you an averagely complicated time -> laplace domain transformation as if its ancient greek then act surprised when you know what it is

[jarviscodinghub]

Solved Quantitative Risk Management Using Copulas, FMSN65/MASM33 Computer Assignment 2

Exercise 1: Some theoretical questions related to copulas Answer the following questions: 1. What are the properties of Archimedean copulas and their generators? 2. Write the bivariate ditribution functions for Frank, Clayton, Gumbel and AMH copulas. 3. Find Laplace transform of a random variable which is distribute as Gamma(a,b) (the density is given in (71) in collection of formulas). Set shape…

[jurjenkvanderhoek]

SHAPE CAME PLAYFUL NOT BY COINCIDENCE

"Coincidence is an event without causality or without known causes. For physicists events are coincidental . If the initial conditions are unknown, prediction cannot be done accurately. For classical physicists coincidence is actually human illusion!"

Does coincidence exist? Factually not. It is an abstract quality. If we do not know the cause we will regard the event that happened to us as a coincidental circumstance.

To rule out coincidence, the probability of a favourable outcome can be calculated with a formula of Laplace. By doing so we learn that the outcome is not from an unforeseen event or just fate. It is no coincidence that my state lottery ticket was a winning ticket. Such a ticket would be a coincidence. But coincidence does notexist according to Laplace. Anyway, that's not going to happen.

Harry van Doveren wrote a text and together with forms of Ankie van Dijk created a quaint book. By chance, his text turns out to be a poem, including squares, curves, lines, debris. No coincidence. Coincidence does not exist, see here above. Each stanza of the poem begins with the word coincidence. That word is then described in plural terms, using synonyms as vices and atomised words as virtues.

Coincidence reflects the right to exist. It looks in the mirror and doesn't see itself, because it doesn't exist, it is not invisible and not without figuration. It is even not present. And yet it has many descriptions and explanations.

Coincidence is attributed to being by people who know neither head nor tail. All they know is that they know nothing. Thinking that the egg came before the chicken. It is a coincidence that the ovum once fell from the sky.

It was foreseenable but arbitrary that the artist and the poet met each other in Ankie van Dijk's first artist book, a pop-up booklet with a harmonica effect. Before the image shows itself, there is the word. After the word the visual matter can be read vertically. By turning the facets, present in three columns, various works can alternately be viewed side by side and put into a relation. Changing order changes this relation, while the tone of the words remains the same.

The collection is bilingual, the images themselves have no boundaries. The poet writes in the language of the Low Countries, Dutch. This does not mean that the collection is restricted to the Dutch realm. Assuming that the poetry is only written in the way it is printed, it concerns sounds without giving meaning to the expression. This tone is like music, a language that everyone speaks. In this way, the reach of this form of art becomes almost limitless. Ankie van Dijk herselfformulates it as follows: "a visual poem demonstrating shapes liberated from perfection. A combinatoric play of forms made for playful readers".

Both views on reality (not fate) offer a chance of success. The poem is not a caption of the form and the form is not an illustration of the poem. Both sexes are closely related to each other as homo ludens. The words are the logo of insight, the emblem of the playing human. By doing the contained vocabulary and imagery in the book might be the result of frolicking, fiddling and fidgeting. The shapes have become the expression of the concept. Converting simplicity in plurality. The words are deliberately accurate prospects, not casually haphazard and unforeseen. Van Doveren has expressed what struck him about Van Dijk's printed works and collages. She plays with form as he plays with language. Together the outcome is both playful as visibly pleasant.

Ankie van Dijk expresses herself in letter-like forms, a form-rich visual language. Simple figurations with multiple expressiveness. Imaginations that remind me of the graphic forms of Hendrik Werkman. The latter, a Dutch book-printer, used lead letters to do the work in his expressionist art. In this way he managed to compose

strong visuals. It is no coincidence that Ankie van Dijk is following his footsteps, or is it coincidence just in this case? I do not know whether she is familiar with Werkman's work. The relationship might be a coincidence, but according to physics, this latter will not be the case.

The powerful symbols are Ankie van Dijk's trademark, such as the axiomatic poetry is the flag under which the ship Van Doveren sets sail. This claim has not been proven but is accepted as a basis. Van Doveren is a beta, so there is no coincidence for him. That is why he can write about it with complete certainty. The retro-avant-gardist Van Dijk comments on the environment with minimal resources. She is guided in her work by Bauhaus and Dada. I indeed recognise modern constructivism in SHAPE.

That visual art and poetry go together is evident from this book (published independently). In every aspect it is deliberately irrational. Words and images undermine the generally accepted presentation standard. Coincidence? No. That would be the style of the Dadaist. You can approach Van Doveren's lines as sound expressions without meaning and intention, only with a recognisable sound and accent. Van Dijk's assemblages are visual expressions without meaning and

purpose, only with a recognisable form and shape.

The German Kurt Schwitters wrote this sound poem Ursonate in 1932: "... Lanke trr gll / pe pe pe pe pe / Ooka ooka ooka ooka / Lanke trr gll / Pii pi pi pi pi / Züüka züüka züüka züüka / Lanke trr gll / Rrmmp / Rrnnf ...." I recognise the same kind of typography and wit in this art-book of van Doveren and Dijk. That can not be a coincidence.

SHAPE by Ankie van Dijk, graphics / 2023

ankiemf@hotmail.com

https://avandijk.exto.nl/

Harry van Doveren, word & design.

harryvandoveren@gmail.com

[erikabsworld]

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The Challenging Question: Consider a circuit with multiple resistors, capacitors, and inductors, interconnected in a complex configuration. You are tasked with analyzing the circuit's behavior under various conditions, including transient and steady-state responses. The question requires a comprehensive understanding of circuit theory, time-domain analysis, and Laplace transforms.

Question: Analyze the given circuit's response to a step input, providing insights into its transient and steady-state behaviors. Additionally, determine key parameters such as time constants and resonance frequencies.

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Laplace Transform Techniques: Employ Laplace transform techniques to simplify the circuit equations. This enables a smoother transition from time-domain analysis to frequency-domain analysis. Derive expressions for voltage and current in terms of Laplace variables.

Steady-State Analysis: Explore the steady-state behavior of the circuit. Identify resonance frequencies and analyze how the circuit responds to sinusoidal inputs. Understand the impact of various parameters on the circuit's frequency response.

Numerical Simulations: Leverage simulation tools like SPICE to validate your analytical findings. This step is crucial for verifying your theoretical calculations and gaining a practical understanding of the circuit's behavior.

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[eulerseverything]

Math history! Let's talk about Leonhard Euler (pronounced Oiler)

I have an arbitrary ruleset I use to decide how prolific a mathematician is. It's not at all actually accurate, but I like it. If you go to a mathematicians wikipedia page and scroll to their known for section in their little side information blurb, most will have a short list of things theyre known for. Some will have a long list (Like Laplace, whos another favorite of mine). Every once in a while, you'll find one that instead of listing everything, links to a separate page that is just their list of contributions. The ones I have found that meet this criteria are Gauss, Erdos, Lagrange, Fermat, and Euler. Euler is special though, because on his page, theres two links, one solely for contributions, and one solely for namesakes.

He's done so much, the list of things hes done and the list of things named after him justify two wikipedia lists. That should give you some idea of this guys level of pure mathematical output, but let me spout some more facts at you.

He published 886 papers in his life. He wrote about 800 papers in a year, or about 500 books throughout his life. His completed works, as far as I'm aware, still aren't published under one book or series of books, because it would be absurdly long. He wrote so much he ended up going blind, then his production INCREASED, after he couldnt see. This is just a bit of trivia a math prof told me that I cant back up, but apparently in the years Euler was active, he published half of ALL MATH PAPERS. One guy makes up half the pie chart for all math papers of the mid 18th century.

He introduced and made mainstream a lot of modern mathematical notation. In mathematics, he founded the studies of graph theory and topology, as well as being influential in other branches such as number theory, complex analysis, and calculus. On top of that, he also did work in tons of other fields, from mechanics to music theory. (this whole paragraph is ripped pretty much directly from wikipedia)

There is no one "Eulers formula" or "Eulers equation", because depending on which specialty in math you ask, they can all give different answers. In my opinion, his most will known contribution is "e", as in base of a natural logarithm, which stands for Eulers number. There is no branch of college level mathematics that you wont eventually stumble into something Euler did or influenced in some way. He is prolific.

My blog is called "Eulers everything" because of simply how many things are called "Eulers ____". There have been times where we credit a discovery to a certain mathematician, then find out Euler actually did it first, in the margins of some notebook or something.

Relevant xkcd

(this isn't the best example in my opinion because there's a significant difference in venn and euler diagrams, but I digress)

I feel like I should have some kind of conclusion here, and I probably could keep spouting fun trivia about just how much this guy has done, but I feel like wrapping it up. My last fun bit of knowledge is he did all of this while also having 13 kids.

Here is your invitation to talk about something in maths you really enjoy. It doesn't matter it's complexity, just reblog with as much or as little detail about one of your favourite things in maths!

[rkdemy]

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[square-enix]

my real christmas gift to myself is not checking on my final grade in differential equations until tomorrow