#Laplace transformation of integrals | Explore Tumblr posts and blogs

carewyncromwell · 2 years ago

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"Started out on a one-way train -- Always knew where I was gonna go next -- Didn't know until I saw your face I was missin' out on every moment..."

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HPHM Cardverse developed by @ariparri // read more about "the Counselor" Duncan Ashe here! // See Jacob as Duncan's Right-Hand Man // credit for the new and improved physics lecture goes to @ag907!! Thank you, sweetie!! 💚

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It wasn't a surprise to much of anyone when Duncan Ashe became the Jack of Spades. He had become a well-respected member of the previous Jack's court even while still at university, and even throughout his schooling, he was known for being both incredibly driven and ambitious. Even if yes, he also became a bit of a rulebreaker upon befriending Coby McQuaid, his strong work ethic and cleverness were never to be questioned. Combine this with a good sense of dress, and most would agree the young man embodied the part of someone who would easily climb the social ladder.

Duncan Ashe knew where he was going. He was going to be successful, and he was going to do it by beating out all of his competition both academically and in life overall. And that is why he took on the responsibility of working under the Jack of Spades, Ulrich Scheller, while also being a full-time student at the University of Spades. It did result in a lack of sleep, sure, and it did make it so he often had to finish homework in strange locations, such as in the middle of press conferences and against the wall of his dormroom while he got dressed in the morning...but it would all be worth it, in the end. Even if he had to finish up complex physics assignments while sitting on the way-too-full trolley heading out of the capitol, Duncan shrugged it off and just kept going.

Or, at least, he did, when he didn't have random strangers standing next to him on the trolley distracting him.

"Physics, huh? That's fun."

Duncan looked up.

Standing over him was a modestly-sized, rather messily-dressed young man about his age with curly dark hair, carrying a beat-up old leather bag at his side. Unlike Duncan, who was dressed in a well-tailored vest and slacks, this person was dressed for hard labor, with his pants tucked into a pair of scuffed-up black boots and faded oil and grease stains on his long-sleeved linen shirt. Even the muscles outlined under his long sleeves were a good indicator that this person was more of a "blue collar" sort than Duncan was.

"What's this? Fourier transforms?" the young man pointed a grubby finger to Duncan’s homework assignment.

Completely taken aback and lost for words, Duncan nodded yes.

"Oh, that's fun!" the stranger said brightly. His almond-shaped blue eyes were very bright as he examined the homework Duncan had in his lap. "You've gotten your sines and cosines mixed up, though -- I think that's what's holding you up on the second one. See, the integral of cosine is sine, not the other way around. Oh, and the answer is supposed to be negative -- we don't use absolute value here. Personally I've always preferred Laplace transforms over Fourier, but they aren't as applicable in physics. The only reason Laplace transforms really took off at all was because of that one fascist prat in Hearts who studied them a long while back -- forgot his name, I'll have to ask Mum -- but even if he was a creep in his politics, he did bring Laplace transforms into the modern era. Reckon people would've had to develop an entirely different way to solve higher order differential equations without them..."

For a moment, all Duncan could do was blink blankly. Finally, like a rubber band, Duncan's surprise and utter disbelief snapped back into defensiveness. He slapped his arms roughly over his work to cover it.

"All right!" he said, his face flushed a bit despite himself. "You've -- you've certainly made your point..."

Duncan couldn't help but goggle a bit.

"Are you a math major or something?" he asked. His black eyes lingered on the boy's dirty shirt and toned arms. Surely not -- any self-respecting university student would have to dress better than this --

The young man, though, only grinned. "Nah, no university for me. I didn't even finish high school."

Duncan's mouth fell open. "You didn't even finish -- ?"

You have got to be kidding me. Some high school drop-out is standing here giving me a lecture about how to do my physics homework?

"Well, the schools up north aren't the greatest -- after a while, I just kind of got fed up," said Jacob. "Plus it's not like getting straight A's or gold stars is any actual indication of intelligence -- it's really more indicative of how well you can jump through hoops, and well, even dumb animals in a circus can do that..."

Duncan flushed, offended.

"And yet those 'dumb animals' could do it, while you couldn't," he said sharply.

"Guess I just like applying my brain to more useful activities," the young man said with a shrug.

"Like fixing mechanical horses and streetcars, I suppose?" Duncan said very dryly, shooting another condescending look at the oil stains on the man's collar.

"Sure," the young man said brightly, not sounding the least bit offended. "Though that's only Mondays and Wednesdays -- got Pik's on Tuesday and Thursday and the library on Fridays..."

He abruptly looked up through the window with slight surprise.

"...Hey, don't you get off here? This is the university."

Duncan realized with a start that the trolley was driving on, passing the university.

With a bolt of panic, he shot up out of his seat, his papers spilling out over the floor so he could get up and pull the string.

"Stop! Stop the trolley!"

The trolley came to a screeching halt. Grumbling in anxiety under his breath, Duncan quickly stuffed his papers into his briefcase and then hurriedly stumbled off the car and off to class.

It wasn't until Duncan took a catalogue of all of his paperwork at home that night that he realized he was missing one page of the physics assignment he'd been working on. He grumbled sourly to Coby about it and the stupid guy on the trolley that made it so he'd now have to do the work all over again for close to a hour, before finally giving up and turning in for the night. He'd just have to work on it tomorrow.

You can imagine Duncan's surprise, therefore, when the following morning, the trolley driver actually handed Duncan a piece of paper after he paid her for the ride as usual.

"Jacob wanted me to give this to you, if I saw you," she said with a wry smile. "He worked on it for the rest of his trolley ride home yesterday -- he saw the due date was in three days, so he hoped I could get it to you before then."

Duncan stared. The page was covered with equations, all scrawled in exquisite detail despite the messiness of the writing.

The stranger who had to be named "Jacob" had finished not only the problem Duncan had been struggling with, but all of them.

~*~

Duncan didn't collide with Jacob again the rest of that week. His hours at Pik's (which turned out to be a tavern -- Coby had heard of it, even if Duncan hadn't) seemed to start very early in the morning, way before Duncan was even out of bed, and whatever library Jacob was assigned to, it must not have been on the route the trolley took into the capitol. Even on the weekend, Jacob was nowhere to be found -- likely taking some well-earned time off at home, Duncan presumed. And so the university student didn't have any potential chance to follow up with Jacob about him having done his work for him until the following week, after Duncan got the assignment back. And when Duncan did see Jacob again, it wasn't on his afternoon trolley ride south to the university -- it was through the trolley's window.

That Monday, Duncan's entire day had gotten off to a terrible start when the trolley's doors had gotten stuck in a half-open position, making it unable to run. As fate would have it, though, Jacob had been at the following stop, and upon being tipped off to the trolley's problem, he ran several blocks up to go help. Soon he'd rolled up his long sleeves and taken a toolkit out of his worn brown bag and immediately set about taking the door apart to fix it.

Duncan looked through the window, tilting his head to try to get a better look at what Jacob was doing.

The curly-haired young man had completely removed the door from the trolley and was now cleaning the interior, scraping out the gunk on the inside and lubricating the rusted hinges with oil. His muscles -- exposed by his rolled-up sleeves -- bulged slightly as he hoisted the door into place and held it there with one arm while screwing the hinge back on with his free hand. His bicep flexed while holding the heavy door, making veins pulse to life through his pale skin.

He was strong.

Duncan caught himself staring and mentally slapped himself. Good thing too, because the very next moment Jacob looked up and caught Duncan's eye through the window.

Jacob blinked, his blue eyes widening just a bit. Then they lit up and he gave a happy little nod, unable to wave due to his hands being full.

"Hey, Ashe!" he greeted.

Duncan was taken aback. "...You know my name?"

"The driver told me," said Jacob. "At least she said she thought that was your name...she caught a glimpse of your student ID once, and she thought it said 'Ashe.' And she reckoned you kind of looked like the rest of the Ashe family -- not that I'd know, never much been anywhere downtown..."

Duncan's lips came together just a bit. He'd never been very close to his family -- his father in particular -- so the reminder that people could see any physical resemblance wasn't particularly cheery.

"The name's Duncan Ashe," he said briskly. "And you would be Jacob, right?"

"Right! Jacob Cromwell," the curly-haired man responded offhandedly.

Duncan raised his eyebrows. "Cromwell? As in the Diamond Empire jewelers?"

Jacob's eyes flashed with dislike. "They're my mum's family. But we don't talk to those prats."

Duncan felt a pang of empathy, thinking of his own family. Something a bit more serious then flickered through Jacob's expression.

"...Were you able to turn in that assignment on time?" Jacob asked. "I hoped you hadn't gotten through it all a second time, by the time you got it back."

Duncan felt his cheeks actually darken with a light flush.

"Oh, ah...yes, I was," he said. He averted his eyes. "I did have to write it out again myself so it'd be in my handwriting, but...what you did was...helpful."

If by "helpful," he meant getting the highest marks he'd gotten in physics class so far.

Jacob gave something of a weak smile. "...Well, I'm sorry you had to write it again -- I'd finished it so you wouldn't have to..."

"Well, yeah, but it wasn't in my handwriting, so someone would've known it wasn't mine, if I'd turned it in that way," Duncan blustered. "Anyway, it...doesn't really matter, it did save me a lot of time, not having to do the math myself. Though I am still a little confused about how you knew how to do it, when you said you never even finished high school."

"I read books in the mathematics section of the library sometimes, during the slower hours," Jacob said with an offhand shrug.

Duncan blinked in surprise.

"You learned all that just from reading library books?" he asked. The courtier couldn't help but be impressed.

"Sure," said Jacob leisurely. "Once you get the theory down, all it really takes is putting it into practice. I just finished up the last of the books on number theory," he added almost as an afterthought. "About a third done with the history section too. Though the science section is actually my favorite to explore -- I recently checked out a book on the biochemistry of various viruses, and it's fascinating. It astounds me that the court of Spades hasn't pushed for using the principle of reverse genetics to develop new vaccines..."

Jacob finally finished screwing the door back into place and, with a bounce in his step, straightened up.

"Go ahead and give it a try now!" he told the trolley driver.

The driver did, and with a ding, the door closed and then opened again like a charm.

Everyone on the trolley burst into applause as Jacob and the other people waiting to board outside all climbed aboard. Several even gave Jacob hearty slaps to the back.

"Thank you so much," the driver said, his blanched face curled up in a weak, relieved smile. "I don't know how I'll ever thank you -- "

"Sounds to me like you just did," Jacob said with a rather handsome smile.

"I've got to at least pay you for your work -- how about -- ?"

"Don't worry about it," said Jacob flippantly.

Without even seeming to notice the driver's attempt to protest, he slid a few coins into the slot by the door to pay for his ride and strolled into the trolley. He sidled into the open seat next to Duncan, grinning broadly. Duncan cocked his eyebrows at the shorter man.

"You could've at the very least accepted a free ride," the well-dressed student pointed out dryly. "The driver was clearly trying to offer it to you."

Then maybe you could save up for some halfway decent clothes, he couldn't help but add to himself, eying Jacob's outfit. It was the exact same one he'd seen him in before, though with perhaps one or two more grease stains.

Jacob blinked. "Really? Huh..."

He shrugged this off very easily, though.

"Oh, well -- I can pay for it, so I may as well. Wasn't doing it for pay in the first place, after all."

Did this guy seriously just shrug off the fact that he could've saved some money when his boots looked like they were a few steps removed from second-hand? Duncan raised his eyebrows.

"Just because you benefited from the trolley being fixed doesn't mean you didn't earn some reward for what you did."

"Oh, I know, but..." Jacob shrugged. "I honestly wasn't even thinking of my own commute, right then. I just knew the driver was having trouble, and I was pretty sure I could help, so I wanted to try. I like solving people's problems," he added with another grin.

Duncan considered Jacob for a moment. It was so strange, how someone who could talk so much about absolutely nothing could come across as so...innocent, in a strange way. So sincere and generous, while also being so clueless about other people's feelings and social cues...

Jacob was a strange person. A strange person, but...interesting.

Little by little, Duncan actually found himself smiling too, though much more wryly.

"...Hm."

Jacob turned his focus to the window as the trolley began to move. Duncan and he fell into a contented silence, which was broken when Duncan initiated conversation again.

"...Which library do you work at?"

"The one uptown, near the museum!" Jacob said with a grin. "My mum recently became a curator there...we generally walk home together those days, so we can pick up Wyn from school on the way. Anyhow, Mum's the most smashing curator -- never been great around lots of people, but she's so smart...she outclasses everyone else there, easily. One day she told me about this new exhibit she's been helping with on the history and short-lived reign of the Knave of Hearts -- bloody as all get out, mind you, but brilliant..."

Before long, Jacob had gone on a long tangent about the history behind the Knave of Hearts's reign and the boom in technological advancements that cropped up in the rest of Cinderhaven in response to refugees fleeing the Kingdom of Hearts. Duncan was having trouble following all of it, but Jacob's passion was remarkable enough to sit through -- it was like sitting beside a raging fire just to enjoy its warmth. And in those times when Duncan found himself on the same wavelength as Jacob, he found a strange excitement pulsing through him as well.

"...And well, out of that, we got new tanks, models of mechanical horses, gas stoves -- even our modern streetcars," said Jacob. "All that, just from immigrants coming here, to explore greater opportunities."

Duncan nodded. "I've put in several proposals to the Jack of Spades, for just that reason."

Not that he's willing to do anything the least bit differently than how they've always been done, he thought dully.

"There's so much potential for growth, if we just invest in projects at home. And if Spades invested more in developing those technologies used for transportation, then it could even encourage other technologically sharp minds in other parts of Cinderhaven to settle here."

Jacob beamed. "Oh, for sure! But you know, I reckon that's only one component, the improving of our transportation methods. It's also about the fuel we use."

"Finding a way to increase coal production to meet demand, you mean?" asked Duncan.

"Yeah, sort of -- but to increase production, we'd also have to make improvements on how it's done," Jacob pointed out. "Coal is smashing and all, but it's still a toxic substance. Prolonged exposure runs the risk of kidney damage, lung damage, heart damage...even it just being too close to running water has proved dangerous. Not to mention coal mines are ridiculously unsafe."

Duncan nodded grimly. The Jack of Spades had received several reports about that, though he'd sort of treated it as "par the course," for such "unskilled" labor.

"So you think the first step would be improving conditions for those coal miners," Duncan surmised.

"Right!" said Jacob. "And well, it wouldn't be too hard! We already have windowed submarines that help us breathe and travel safely underwater...all we'd really need is a way to adapt that concept for use in mines! Some sort of a submarine suit, for use underground instead of underwater...oh!"

The curly-haired man abruptly shot to his feet and grabbed the string, tugging down on it sharply to tell the trolley to stop. Duncan looked up, startled, as the trolley came to a stop right outside the university.

"Didn't want you to miss your stop," said Jacob with a slightly cheeky smile.

"I suppose it is the least you can do," Duncan said coolly, "considering you almost made me miss my stop for a second time."

He got to his feet and headed for the trolley door. In the door frame, though, he paused, and he glanced back at Jacob.

"...You work at Pik's Tavern, right?" he asked.

Jacob blinked. "Yeah -- Tuesdays and Thursdays."

Duncan's lips curled up into a very small smirk. "I'll try to pop in sometime. I could use a place to eat with a good discount...that is, if knowing a guy there would put me in good standing?"

Jacob beamed so brightly that his blue eyes actually sparkled a bit.

"10% off your order, if you ask for me by name!" he said brightly.

Duncan's smirk broadened a bit. "10%? That's not bad. All right -- tomorrow morning, then, before I head into work."

"It's a date, then!" Jacob called back, as Duncan finally climbed off the trolley.

Once he'd stepped off, Duncan found his eyes darting up to the trolley as it closed its doors and drove off. He also found his heart beating just that little bit faster and his cheeks flushing as he brought a hand through his hair, looking away again quickly.

A date, then, he recurred Jacob's offhand remark in his own head. Duncan tried to push the memory down, even as it made his lips spread into an amused smile.

Obviously he'd never date an idiot like Jacob Cromwell...but talking with him some more would be fun. It'd be like spending time with Coby, back in grade school -- except with someone who couldn't read social cues and went on ridiculous, rambling tangents about absolutely nothing...

But it could be fun. Listening to Jacob get carried away by his own passions and getting a bit swept up in them himself for a while...that could be fun.

~*~

That day Duncan ended up bringing up the idea of applying reverse genetics to future vaccinations during a meeting with the Jack of Spades and his other courtiers. It was an idea that prompted an muted nod of approval from the Jack, as well as a few side-long glances from the other courtiers that made it clear they wished they'd proposed the idea.

Jacob would've probably been blissfully unaware of those envious looks, Duncan thought to himself in amusement. He probably would've also gone a whirlwind tangent about how to apply the same vaccination principles to the farming of produce or something.

~*~

When Duncan visited Pik's Tavern the following morning, he wasn't served by Jacob, as he'd expected -- instead, after eating one of the best breakfasts he'd had in his life, Duncan found a scrawled note on the receipt his female server had brought him.

10% off, as promised! Hope I cooked the eggs all right -- if you'd like them runnier next time, just let me know. Jacob C

The bloke could cook. The knowledge made Duncan stare at the little note on the receipt a bit longer than he should've.

After stewing in his thoughts for a moment, Duncan finally decided to bite the bullet and ask his server about when Jacob got off work. The server gave him a knowing smile.

"He's supposed to only work mornings," she explained, "but he always stays later. I reckon Jacob would stay and work for a full twelve hours, if we'd let him...but he always heads out, whenever his sister gets here."

Duncan blinked. "His sister?"

The memory of Jacob mentioning a "Wyn" rippled over his mind.

"Carewyn's her name," said the server fondly. "She's a sweet little thing -- smarter than her brother too, sometimes. She's still in grade school, but she always takes the trolley after school to 'pick Jacob up' when he's working here, so they can head home together." She gave a soft laugh behind her hand. "It's absolutely adorable."

The thought of Coby carrying his sister Veruca on his shoulders when she was little rippled over Duncan's mind, and it made something a little softer flit through his expression.

"...I see..."

Well, there went the idea of talking to Jacob some more after he got off work... Duncan considered his options for a moment before speaking again.

"...I'll be off then," he said at last, his voice incredibly business-like. "Tell Jacob I'll be back Thursday morning -- and if possible, I'd like to give him a review of his cooking in person."

~*~

From then on, Duncan would come into Pik's Tavern every Tuesday and Thursday morning on his way into the capitol, Jacob would cook him a scrumptious breakfast spread, and they would talk while Duncan ate. More than once Duncan would pay for Jacob's meal too so that he could eat with him -- if nothing else, he said gruffly, he should reimburse the Tavern for "stealing" one of their chefs for an hour or so twice a week.

As he and Jacob sat together, they would talk about various things -- economics, dirigibles, medicine, anthropology, music, renewable energy, joke shops, trains, mythology, biodegradable alternatives to household goods...anything and everything. They'd also talk about themselves, sometimes. Jacob would gush about his sister Carewyn, who was as sweet and small as a cherub, but brave and smart as a whip, and his mother Lane, who was soft-spoken and hated crowds, but was the gentlest and smartest person he knew. Duncan would talk about Coby -- about how laid-back and fun he was to be around, about all the trouble they got into at school together...about how much he loved his sister Veruca, and how much Jacob had reminded him of his best friend. Duncan would talk about his father and how they never spoke after the death of his mother -- how Duncan was working at the court of Spades and was determined to really be somebody, his own person, on his own and successful and free to do as he liked. Jacob would talk about how his father abandoned his family, leaving Jacob to drop out of school so as to help keep his family afloat financially through his multiple part-time jobs, and how he taught himself using books from the library, since he lacked the money or qualifications to attend university himself. Sometimes Jacob would even sing! Duncan caught the other man's tenor voice echoing several times out of the kitchen on his way out to greet him, and each time the soaring, carefree tone would make Duncan's heart skip a beat.

The two young men would talk and talk until finally both Jacob and Duncan had cleared their plates and had to get back to their respective jobs. And at Duncan's job in particular, he found the subjects of his meetings with Jacob returning to his mind more and more, whenever he'd meet with the rest of court.

"If we're looking for funds for these projects," Duncan proposed one day, "then perhaps technology could provide some solutions. Sure, we don't have enough money to pay for a new school right now...but investing in energy that's renewable, rather than single-use, could make it cheaper to refuel the machines needed to build these new structures. Water, for instance -- it's still only been used on the large scale right now with dams, but hydroelectric power could be a great alternative, if it could be duplicated on a smaller scale."

Afterward the Jack of Spades actually pulled Duncan aside to speak to him privately.

Ulrich Scheller was a very austere, by-the-book sort of man. Duncan had never once see him smile, and he and Coby both reckoned no one had ever heard him crack a joke in his life. Ulrich was very tall and stiff-shouldered, dressed in a high-necked black and white tweed coat that made him look like a vicar. He was losing some of his blond hair, so he'd combed his gelled hair down a bit to obscure it, but it didn't appear comical: if anything, it only made his forehead appear taller and his face appear longer and pointier, by extension.

"Your idea is really quite inventive," said the older man, his eyes boring into Duncan very carefully. "I hope you don't mind if I discuss it with the King, when next I speak with him?"

Duncan was startled. The Jack actually wanted to tell the King about something he'd suggested?

"Of course not," he said very quickly, once he'd recovered.

"Good," said Ulrich.

He crossed his arms behind him, strolling over to the window and looking out.

"...The King was very positive, when someone passed along your idea about vaccines. He came to me specifically requesting that I invest more in our local laboratories for the coming year. ...I don't think I've ever heard the King speak so passionately about infrastructure before."

The Jack's eyes watched Duncan's reflection in the window carefully. Duncan felt like an invisible hand was squeezing his stomach in a vice grip.

"...Thank you," Duncan said after a moment.

"Your hard work and resourcefulness have garnered quite a lot of attention," the Jack pressed on. "Investing in biodegradable tools, applying submarine technology to mining equipment...even the Ace of Spades has noticed. I think I even caught her expressing some interest in some of your ideas -- or at least, adapting them for her particular department..."

Ulrich gave Duncan an almost curious look.

"I must admit, Mr. Ashe...you are an impressive young man."

Duncan felt ill.

The praise should've been so validating -- after all, Duncan had worked incredibly hard, and he did want to be seen as valuable to the Court of Spades...but he'd only brought up Jacob's ideas because they were objectively good ideas -- they had to be, if the King reacted so well to them! Duncan hadn't really planned to take sole credit for those ideas...and now that he was set to, he found himself feeling trapped. On the one hand, he didn't want to take credit for ideas that Jacob had come up with all by himself, without even a formal education...but on the other hand, he didn't know how the Jack of Spades would respond to the knowledge that Duncan had earned all of this respect through promoting ideas developed by someone else...

"Mr. Ashe?" said Ulrich. "Is something the matter?"

Duncan shot out of his reverie. "No, sir."

He paused. Jacob's grinning face swam over his mind.

"Guess I just like applying my brain to more useful activities."

"Wasn't doing it for pay in the first place, after all."

"I honestly wasn't even thinking of my own commute, right then. I just knew the driver was having trouble, and I was pretty sure I could help, so I wanted to try. I like solving people's problems."

Jacob never looked for any kind of reward, for the work he put in. He didn't ever seem to want anything selfishly for himself. All he ever seemed to care about was solving problems -- knowing that what he'd done had been helpful to others...

Even so...

Duncan swallowed.

"...I can't take credit for those ideas, sir," he admitted lowly at last. "All I did was share them -- "

"Shared them at very critical moments," Ulrich cut him off smoothly. "They were timely and educated suggestions. You clearly put a lot of thought into them..."

"No, I didn't," Duncan said, a bit more loudly than he meant.

He very quickly reigned his emotions back in as best he could.

"...I mean, yes, they were applicable to the task at hand -- and yes, I have worked hard, and I appreciate you noticing..."

The young man swallowed again, trying to steady his courage.

"...But those ideas...I didn't come up with them on my own. They weren't even my ideas in the first place -- they're someone else's."

Duncan averted his eyes, unable to look at his superior.

"...He's the inventive one. I just...recalled his ideas, during those conferences."

The Jack of Spades considered Duncan for a long moment. Then, to Duncan's shock, he actually smirked slightly.

"Mr. Ashe," Ulrich said coolly, "you misunderstood my compliment completely. I never expected all of those ideas to be solely your own invention -- for however smart you fancy yourself to be, you are still only a student," he added rather dryly. "You have so much still to learn -- about politics, about the world. About mankind overall. That's why it's a remarkable talent, to discern which voices to listen to...to pinpoint good ideas when you hear them and promote them to others who might be too afraid to pursue them, despite their novelty. ...It's a talent I've lacked for a very long time..."

The Jack turned around to face Duncan properly, his arms still folded stiffly behind him.

"Yes, perhaps others presumed these ideas were fully germinated from your brain, but I was never so foolish to. Speaking from experience, however -- there's nothing inherently wrong with being influenced by the people around you, especially if they are both valuable and trustworthy. And from the sound of things...the people who've inspired you have been fortunate enough to earn your trust."

Duncan felt that hand squeezing his stomach loosen its grip. He relaxed slightly, relieved that his position hadn't been compromised -- but there was still something restless, in his feet.

"...Thank you, sir," he said.

Duncan paused. Then, after a moment, he spoke with a big more strength in his voice.

"Sir?"

"Yes?"

"There's this man I know. He's my age, but his mind...it's inventive, truly inventive, in a way mine isn't. ...I think he'd be invaluable, in developing new interior projects for the Country of Spades."

Ulrich cocked his eyebrows, interested.

"If you think so, perhaps you should invite him to court."

Duncan's heart gave a leap of surprise as Ulrich strolled over to the door of his office.

"...You give your approval, sir?" Duncan asked, delighted.

"After tonight, Mr. Ashe," the Jack said cryptically, "I don't think you'll need it."

He didn't explain himself at all before he strode away.

It was only when Duncan returned home that he found the official Spades-sealed letter that had been delivered to his door.

Dear Mr. Ashe, We are pleased to inform you that you have been nominated -- with nearly universal approval from the Court of Spades -- to take on Master Ulrich Scheller's position as the Jack of Spades.

~*~

Within a few weeks, Duncan had taken on the mantle of the new Jack of Spades. The same day Duncan was inaugurated, Jacob Cromwell put in his letter of resignation at the mechanic shop, Pik's Tavern, and the uptown library near his home and took a full-time job as an advisor and technology expert at the court of Spades under Duncan.

The rest of the courtiers honestly didn't know what to make of Jacob at first, but fortunately even those who'd looked upon him with the most scorn eventually came to see how truly brilliant the young man was. More than a few times, Patricia Rakepick tried to coax Jacob to make some more militaristic modifications to his blueprints -- but to Duncan's satisfaction, Jacob always ended up finding a way to blow the Ace of Spades off.

"Why would you use mining suits on a battlefield anyway?" Jacob asked with a deep frown. "They'd get trashed up so fast you'd have to fix them over and over...so pointless..."

Duncan smiled wryly. "Guess I shouldn't be surprised you have more interest in building mechanical bees than bombs and tanks."

"Well, of course!" said Jacob as if it were obvious. "Mechanical bees can help with the shrinking bee population. With artificial pollinators in the mix, we can both help the environment and improve food and medicine production! Not to mention the technology could be applied to larger models, once it's perfected -- imagine! Mechanical winged horses that can pull our own modified flying carriages! Mechanical carrier pigeons to deliver messages! Maybe even mechanical dragons! Imagine the uses that could give to a welder, or a baker...anyone in the culinary industry, really..."

Duncan found himself smiling absently as he let Jacob go off on another one of his dreamy tangents. His subordinate's blue eyes had drifted skyward ages ago, as it often did whenever he was thinking hard, but they sparkled like happy aquamarine gems.

Jacob hadn't had a lot of opportunities in his life, prior to meeting Duncan. After meeting him, though, Duncan hoped he'd have more, much more.

Because someone this resilient...this brilliant, this passionate, this idealistic and good...even with all the disadvantages he'd had and all the struggles he'd had to overcome and all the reasons he had to resent the world and his place in it...

He deserved to be celebrated. He deserved to be great, and appreciated, and successful -- to be able to do what he wanted to do and chase all of his sky-high dreams as far as they'd take him...

Jacob deserved to feel important. Because...he was. To Duncan, at the very least...he was important.

#cardverse au #hphm cardverse #duncan ashe #jacob cromwell #my writing #coby mcquaid #veruca mcquaid #carewyn cromwell #graaaaah I love these two so much #doesn't matter what universe #LMAO though duncan I see you eying my boy #1) bad fashion but cute 2) smart AF 3) muscles 👀👀👀 4) CAN COOK OMG 5) wubs his sis like my BFF awwww #you are so whipped boy hahahaha

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drmikewatts · 4 months ago

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IEEE Transactions on Fuzzy Systems, Volume 33, Issue 2, February 2025

1) Distributed Saturation-Tolerant Fuzzy Control for Constrained Stochastic Multiagent Systems With Resilient Quantitative Behaviors

Author(s): Xiaohui Yue, Huaguang Zhang, Jiayue Sun, Lulu Zhang

Pages: 514 - 523

2) Bayesian Weighting for Multiple Criteria Group Decision-Making With Interval Preference Information

Author(s): Fan Liu, Huchang Liao

Pages: 524 - 536

3) Adaptive Integral Sliding-Mode Control for a Class of Nonlinear Spacecraft Proximity Systems Under Multi-Source Disturbances and Unmodeled Dynamics

Author(s): Yuan Zhu, Xin Ning, Zheng Wang, Caisheng Wei, Shichao Ma, Likuan Qiu, Shiyu Wang, Yunfei Bai

Pages: 537 - 548

4) Hierarchical Fuzzy Model-Agnostic Explanation: Framework, Algorithms, and Interface for XAI

Author(s): Faliang Yin, Hak-Keung Lam, David Watson

Pages: 549 - 558

5) Fixed-Time Event-Triggered Impulsive Secure Synchronization of Quaternion-Valued Fuzzy Neural Networks Subject to Stochastic Cyber-Attacks

Author(s): Lirong Liu, Haibo Bao, Jinde Cao

Pages: 559 - 569

6) Adaptive Fuzzy Control for Stochastic Nonlinear Systems With Delayed Input and Delayed State via Improved Lyapunov–Krasovskii Function

Author(s): Yanru Peng, Shengyuan Xu, Ju H. Park

Pages: 570 - 579

7) Reinforcing TSK Model Interpolation With Rule Weight Adjustment via Location View Analysis

Author(s): Changhong Jiang, Changjing Shang, Qiang Shen

Pages: 580 - 592

8) Parameter-Optimization-Based Adaptive Fault-Tolerant Control for a Quadrotor UAV Using Fuzzy Disturbance Observers

Author(s): Yong Ren, Yaobin Sun, Zhijie Liu, Hak-Keung Lam

Pages: 593 - 605

9) A Terminal Constraint Set-Dependent Mixed Time/Event-Triggered Approach to Multistep Fuzzy MPC

Author(s): Fan Wei, Xiongbo Wan, Chuan-Ke Zhang, Leimin Wang

Pages: 606 - 620

10) Fuzzy-Based Antiswing Control for Variable-Length Cable-Suspended Aerial Transportation Systems Considering the Hook Effect

Author(s): Hai Yu, Yi Chai, Zhichao Yang, Jianda Han, Yongchun Fang, Xiao Liang

Pages: 621 - 630

11) A Brain-Inspired Harmonized Learning With Concurrent Arbitration for Enhancing Motion Planning in Fuzzy Environments

Author(s): Tianyuan Jia, Chaoqiong Fan, Qing Li, Ziyu Li, Li Yao, Xia Wu

Pages: 631 - 643

12) From Fuzzy Rule-Based Models to Granular Models

Author(s): Ye Cui, Hanyu E, Witold Pedrycz, Zhiwu Li, Xianmin Wang

Pages: 644 - 656

13) Adaptive Fuzzy Distributed Optimal FTC for Nonlinear Multiagent Systems Based Multiplayer Differential Game

Author(s): Wei Wu, Shaocheng Tong

Pages: 657 - 668

14) Scalable Feature Subset Selection With Fuzzy Rough Sets and Fuzzy Min–Max Neural Network in Hybrid Decision System

Author(s): Anil Kumar, P. S. V. S Sai Prasad

Pages: 669 - 679

15) Minimum Adjustment Consensus Optimization Models With Fuzzy Preference Relations: The Perspective of Cardinal and Ordinal Consensus

Author(s): Zhengmin Liu, Wenxin Wang, Ruxue Ding, Peide Liu

Pages: 680 - 693

16) A Novel Composite Observer Based Approach for Dynamic Event-Triggered Adaptive Fuzzy Control of Nonlinear Systems Under DoS Attacks

Author(s): Xinjun Wang, Shenghang Liu, Ben Niu, Xinmin Song, Huanqing Wang, Xudong Zhao

Pages: 694 - 703

17) Observer-Based Optimal Fuzzy Control for Networked IT-2 Fuzzy Systems Against Hybrid Cyber-Attacks

Author(s): Yang Li, Ju H. Park, Yang Gu, Yong He

Pages: 704 - 716

18) Generalized Fuzzy Transform and Nonlocal Laplace Operator

Author(s): Hana Zámečníková, Simone Cammarasana, Irina Perfilieva, Giuseppe Patané

Pages: 717 - 729

19) Dual Anchor Graph Fuzzy Clustering for Multiview Data

Author(s): Wei Zhang, Xiuyu Huang, Andong Li, Te Zhang, Weiping Ding, Zhaohong Deng, Shitong Wang

Pages: 730 - 744

20) Fuzzy Secure Formation Control for NMASs: A Prescribed Performance Scaling Framework

Author(s): Dianbiao Dong, Jiahe Huo, Tao Xu, Dengxiu Yu, Zhen Wang

Pages: 745 - 756

21) A ZNN-Based Solver With Adaptive Input Range Fuzzy Logic System for Time-Varying Algebraic Riccati Equation

Author(s): Lin Xiao, Dan Wang, Qiuyue Zuo, Xiangru Yan, Hang Cai

Pages: 757 - 766

22) Fuzzy Min-Cut With Soft Balancing Effects

Author(s): Huimin Chen, Runxin Zhang, Rong Wang, Feiping Nie

Pages: 767 - 778

23) Distributed Fuzzy Formation Control for Nonlinear Multiagent Systems Under Communication Delays and Switching Topology

Author(s): Haodong Zhou, Yi Zuo, Shaocheng Tong

Pages: 779 - 788

24) Observer-Based Predefined-Time Adaptive Fuzzy Prescribed Performance Tracking Control for a QUAV

Author(s): Guozeng Cui, Guanchao Zhu, Juping Gu, Qian Ma, Shengyuan Xu

Pages: 789 - 798

25) Disturbance Observer-Based Boundary Adaptive Event-Triggered Consensus Control of Multiple Flexible Manipulators

Author(s): Wei Zhao, Xiangqian Yao, Yu Liu

Pages: 799 - 809

#ai #artificial intelligence

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syn-odics · 5 months ago

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whenever the mcelroys bring up heavyside, meaning cats, I get very confused bc I start thinking about Laplace transform integrals

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iit-jam · 6 months ago

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IIT JAM Syllabus 2025: A Comprehensive Guide

The IIT JAM (Joint Admission Test for Masters) is one of the most competitive exams for students aspiring to pursue postgraduate studies in esteemed institutions like IITs and IISc. Mathematics, being a core subject, attracts candidates with strong analytical and problem-solving skills. To excel in this exam, a thorough understanding of the IIT JAM Mathematics Syllabus 2025 is essential. This blog outlines the syllabus in detail and provides tips to help candidates prepare effectively.

Overview of IIT JAM Mathematics Syllabus 2025

The IIT JAM Mathematics Syllabus 2025 is crafted to test the candidates' knowledge of fundamental mathematical concepts covered at the undergraduate level. The syllabus is broad, covering topics such as calculus, linear algebra, differential equations, and numerical analysis. Each section focuses on key areas that are crucial for advanced studies and professional applications.

Key Topics in the Syllabus

1. Sequences and Series

This section includes the convergence of sequences and series, tests for convergence (such as comparison, ratio, and root tests), and the study of power series and their radius of convergence.

2. Differential Calculus

Candidates must understand single-variable calculus concepts like limits, continuity, and differentiability. Topics also include Taylor series, mean value theorem, and indeterminate forms. For multivariable calculus, partial derivatives, maxima, minima, saddle points, and the method of Lagrange multipliers are essential.

3. Integral Calculus

This section covers definite and indefinite integrals, improper integrals, and special functions like beta and gamma functions. The application of double and triple integrals is also emphasized.

4. Linear Algebra

A critical area of the syllabus, it focuses on vector spaces, subspaces, linear transformations, rank, nullity, eigenvalues, eigenvectors, and matrix diagonalization. Understanding the solution of systems of linear equations is vital.

5. Real Analysis

This section involves the properties of real numbers, limits, continuity, differentiability, and Riemann integration. Candidates must also be familiar with sequences, Cauchy sequences, and uniform continuity.

6. Ordinary Differential Equations (ODEs)

This includes first-order ODEs, linear differential equations with constant coefficients, systems of linear ODEs, and Laplace transform techniques for solutions.

7. Vector Calculus

Important topics include gradient, divergence, curl, line integrals, surface integrals, and volume integrals, along with Green’s, Stokes’, and Gauss divergence theorems.

8. Group Theory

The basics of groups, subgroups, cyclic groups, Lagrange’s theorem, permutation groups, and homomorphisms are covered.

9. Numerical Analysis

This section focuses on numerical solutions for non-linear equations, numerical integration and differentiation, interpolation methods, and error analysis.

Tips for Preparing the Syllabus

Understand the Weightage: Review past papers to prioritize high-scoring topics like Linear Algebra, Real Analysis, and Differential Calculus.

Strategize Your Study Plan: Divide the syllabus into manageable sections, set achievable goals, and stick to a consistent schedule.

Practice Regularly: Solve previous years’ papers and mock tests to familiarize yourself with the question patterns and improve speed.

Strengthen Fundamentals: Focus on core concepts by revisiting undergraduate textbooks and seeking clarity on challenging topics.

Leverage Online Resources: Utilize tutorials, study materials, and practice tests available online to supplement your preparation.

Conclusion

The IIT JAM Mathematics Syllabus 2025 is extensive yet well-structured, providing a clear framework for aspirants to plan their preparation. By mastering the syllabus and practicing diligently, candidates can confidently tackle the exam and achieve their dream of joining top postgraduate programs. Dedicate time, stay consistent, and focus on strengthening your mathematical foundations to excel in IIT JAM Mathematics 2025.

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coursesfe · 10 months ago

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Key Topics to Focus on for the FE Electrical Exam

Preparing for the Fundamentals of Engineering (FE) Electrical and Computer exam is a crucial step toward a successful career in engineering. The FE Electrical exam, administered by the National Council of Examiners for Engineering and Surveying (NCEES), tests your knowledge and understanding of fundamental electrical engineering concepts. Effective FE Electrical exam preparation involves focusing on key topics that are integral to passing the exam. Here’s a breakdown of essential areas to concentrate on to ensure you’re well-prepared.

Circuit Analysis

Circuit analysis is a fundamental topic in the FE Electrical exam. You should have a solid understanding of both AC and DC circuit principles. Key areas include Ohm’s Law, Kirchhoff’s Voltage and Current Laws, and Thevenin and Norton equivalent circuits. You will need to solve problems involving resistors, capacitors, inductors, and their interactions in various circuit configurations. Mastering these concepts will help you tackle circuit analysis questions efficiently.

Electronics

Electronics is another critical area of focus. The exam will test your knowledge of semiconductor devices such as diodes, transistors, and operational amplifiers. Understanding the operation, characteristics, and applications of these components is vital. Be familiar with different configurations and circuits involving these devices, including amplifiers, oscillators, and rectifiers.

Electrical Machines and Power Systems

Knowledge of electrical machines and power systems is essential for the FE Electrical exam. This section covers topics like transformers, induction motors, synchronous machines, and their operation principles. Additionally, you should be comfortable with power generation, transmission, and distribution concepts, including the understanding of power factor, three-phase systems, and fault analysis.

Signals and Systems

The FE Electrical exam includes questions on signals and systems, which are fundamental in electrical engineering. Focus on understanding signal processing techniques, including Fourier series, Fourier transforms, and Laplace transforms. Knowledge of system stability, linear time-invariant systems, and convolution is also important.

Electromagnetics

Electromagnetic theory forms a significant part of the FE Electrical exam. Key topics include Maxwell’s equations, electromagnetic waves, and transmission lines. Understanding concepts such as electric fields, magnetic fields, and their interactions is crucial for solving problems related to electromagnetics.

Control Systems

Control systems are integral to many engineering applications. In your FE Electrical exam preparation, concentrate on feedback control systems, stability analysis, and control system design. Familiarize yourself with transfer functions, block diagrams, and the basics of control theory to handle questions related to control systems effectively.

Mathematics

Strong mathematical skills are essential for the FE Electrical exam. Focus on calculus, differential equations, linear algebra, and probability and statistics. These mathematical concepts are frequently used in solving engineering problems and are critical for analyzing and interpreting data.

General Engineering Concepts

In addition to the specific topics mentioned above, make sure you have a good grasp of general engineering principles. This includes engineering economics, ethics, and professional practice. Understanding these topics will help you navigate the broader aspects of engineering practice that may be covered in the exam.

Conclusion

Effective FE Electrical exam preparation requires a strategic focus on key topics that are frequently tested. By concentrating on circuit analysis, electronics, electrical machines and power systems, signals and systems, electromagnetics, control systems, mathematics, and general engineering concepts, you will be well-equipped to tackle the challenges of the FE Electrical exam. Utilize comprehensive study materials and practice exams to reinforce your knowledge and improve your problem-solving skills. For additional support and resources, consider enrolling in the FE Electrical and Computer Exam Preparation Course offered by StudyForFE. This course provides targeted preparation to help you succeed on your path to becoming a licensed professional engineer.

#fe electrical

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studyforfe · 11 months ago

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Essential Topics for the FE Electrical and Computer Exam

The FE Electrical and Computer Exam, administered by the National Council of Examiners for Engineering and Surveying (NCEES), is a crucial step for aspiring engineers aiming to become licensed professional engineers. This exam covers a broad range of topics and requires thorough preparation. Understanding the essential subjects is key to achieving success. In this article, we will explore the critical areas that every candidate should focus on for the FE Electrical and Computer Exam.

Mathematics

Mathematics forms the backbone of the FE Electrical and Computer Exam. Topics include calculus, differential equations, linear algebra, and probability and statistics. Candidates must have a strong grasp of mathematical concepts as they are applied throughout various sections of the exam. Proficiency in these areas is essential for solving complex engineering problems.

Circuit Analysis

Circuit analysis is a fundamental topic for the FE Electrical Exam. This includes understanding Ohm's Law, Kirchhoff's laws, Thevenin and Norton equivalents, transient and steady-state analysis, and AC/DC circuits. Candidates should be able to analyze and design both simple and complex circuits, as this knowledge is crucial for various practical applications in electrical engineering.

Electronics

Electronics is another critical subject area. The FE Electrical and Computer Exam covers topics such as diodes, transistors, operational amplifiers, digital logic, and analog circuits. Understanding the behavior and application of electronic components is vital for tasks ranging from circuit design to troubleshooting.

Power Systems

Power systems are a significant focus in the FE Electrical Exam. Topics include power generation, transmission, distribution, transformers, and three-phase systems. Candidates should understand the principles of electrical power, including the analysis and design of power systems, to ensure efficient and reliable delivery of electricity.

Control Systems

Control systems are essential for the automation and regulation of processes. The FE Electrical and Computer Exam tests knowledge of feedback systems, transfer functions, stability analysis, and controllers. Understanding these concepts is crucial for designing systems that maintain desired performance levels despite disturbances.

Signal Processing

Signal processing involves the analysis, manipulation, and interpretation of signals. Key topics include Fourier transforms, Laplace transforms, Z-transforms, and filtering. This knowledge is applied in various fields such as telecommunications, audio engineering, and image processing. Mastery of signal processing techniques is important for handling and improving signal quality.

Electromagnetics

Electromagnetics is a challenging but essential topic for the FE Electrical Exam. This area covers Maxwell's equations, wave propagation, transmission lines, and antennas. A solid understanding of electromagnetics is necessary for tasks involving the design and analysis of communication systems, radar, and other applications involving electromagnetic fields.

Computer Systems and Software

With the increasing integration of computer systems in engineering, this topic has gained prominence in the FE Electrical and Computer Exam. Candidates should be familiar with computer architecture, operating systems, programming, and software engineering principles. This knowledge is crucial for developing and maintaining efficient and effective software solutions.

Communications

The communications section of the FE Electrical Exam encompasses analog and digital communication systems, modulation techniques, and information theory. Understanding the principles of how information is transmitted and received is vital for designing and optimizing communication networks.

Conclusion

Preparing for the FE Electrical and Computer Exam requires a comprehensive understanding of a wide range of topics. Focusing on the essential areas outlined above will provide a strong foundation for success. By mastering subjects such as mathematics, circuit analysis, electronics, power systems, control systems, signal processing, electromagnetics, computer systems, and communications, candidates can approach the exam with confidence. For more detailed study resources and guidance, visit StudyforFE.com.

#FE Electrical and Computer

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erikabsworld · 1 year ago

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Mastering Linear System Modeling: A Step-by-Step Guide

Are you struggling with linear system modeling assignments? Do you find yourself lost in a maze of equations and concepts? Fear not! In this comprehensive guide, we'll demystify linear system modeling and provide you with a step-by-step approach to tackle even the toughest assignment questions. Let's dive in!

Understanding Linear System Modeling

Linear system modeling is a fundamental concept in various fields such as engineering, physics, economics, and more. It involves representing real-world systems using mathematical models to analyze their behavior and predict outcomes. These systems can range from electrical circuits to chemical processes to economic markets.

At its core, linear system modeling deals with relationships between inputs and outputs of a system, assuming linearity, which means the output is directly proportional to the input. This simplifies the analysis and allows for the use of powerful mathematical tools like matrix algebra and differential equations.

Sample Assignment Question:

Consider a spring-mass-damper system with the following properties:

Mass (m) = 1 kg

Spring constant (k) = 10 N/m

Damping coefficient (c) = 2 Ns/m

Given an external force (F(t)) of 5 N acting on the system, find the equation of motion and determine the system's response.

Step-by-Step Guide:

Understand the System: Before diving into calculations, it's crucial to understand the system's components and behavior. In this case, we have a spring (providing restorative force), a mass (subject to inertia), and a damper (dissipating energy).

Formulate the Equation of Motion: The equation of motion for this system can be derived using Newton's second law, which states that the sum of forces acting on an object equals its mass times acceleration (F = ma). In our case, the equation is: m(d^2x/dt^2) + c(dx/dt) + kx = F(t) . Where x represents the displacement of the mass from its equilibrium position.

Solve the Differential Equation: This is where we apply mathematical techniques to solve the differential equation obtained in the previous step. Depending on the nature of the external force (F(t)), solutions can vary. Common methods include Laplace transforms, numerical integration, or analytical solutions for simpler cases.

Analyze the System's Response: Once we have the solution for x(t), we can analyze the system's behavior over time. This includes studying transient and steady-state responses, stability, frequency response, and any other relevant characteristics.

How We Can Help:

At matlabassignmentexperts.com, we understand the challenges students face when dealing with complex topics like linear system modeling. That's why we offer expert linear system modeling assignment help to guide you through your assignments, ensuring clarity and accuracy in your solutions. Our team of experienced tutors is dedicated to providing personalized support tailored to your specific needs, helping you excel in your studies and achieve academic success.

In conclusion, mastering linear system modeling requires a solid understanding of the underlying principles and a systematic approach to problem-solving. By following the steps outlined in this guide and seeking assistance when needed, you can confidently tackle any assignment question that comes your way. Remember, practice makes perfect, so don't hesitate to put your newfound knowledge to the test!

#assignment help #help with assignments #matlab assignment help #education

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exam-daikao · 1 year ago

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代写之家接过的留学生代考科目代码，实力强，经验足！好成绩显而易见，擅长数学物理化学经济金融计算机电气等专业

代写之家创办11年以来，接过无数的留学生考试，作业的代写代考代做单子，经验之丰富不是一般野鸡机构能比拟的。每次接单之前，我们都会对学生给出的资料进行详细的评估，而后做出是否能胜任的决定，绝不是一般同行碰到单子就满口承若接下，压根不去做接单前的资料评估而随意接单，导致后续考试时候做不出任何题目，也请大家擦亮眼睛，多花点耐心去甄别所托之人是否负责靠得住。代写之家将继续秉承“一次合作，终生朋友”的信念服务好大家，继续为家人们的学业保驾护航！以下是我们实际接过的部分科目代码详情，由于篇幅有限，不能把所有科目课程列举完毕，仅供大家参考，看下有无自己实际需要的科目。学生范围覆盖了美国，加拿大，英国，澳大利亚，新加坡，德国，俄罗斯，意大利，瑞士等国际，以及香港，澳门，台湾地区。科目范围涵盖了数学，物理，化学，经济学，金融学，计算机，电气工程等本硕方向的专业。数学类：Pre-Calculus Math 12，MATH 1014 Calculus II，MATH2011 Intro to Multivariable Calculus ，Math 221 Calculus I，MA 1201，Math 231.Calculus ll，Math 241 Calculus III，MAT236，MATA37 Calculus，MAT232 Calculus of Several Variables，Math 1B - Calculus，MATH2323 GENERAL MATHEMATICS 1，MAST10006 Calculus 2 MAST10006 Calculus 2，MATH 53 Multivariable Calculus，Math 151 — Calculus II，Math 20E，MATH 152，MATH 156 - Calculus for Business and Economics II，Math 3140/2310，Math 10C，Math 263，Math 1322 ，Math1206，Math 2300 Calculus III，MA 411，Math 125，ENG2005 Advanced Engineering Mathematics，MA2006 Real Analysis，MAT 2125 Elementary Real Analysis，Math 597 REAL ANALYSIS，Math 3050/6050，Math UA 325 Real ，MATHEMATICS 2A VECTOR CALCULUS & COMPLEX ANALYSIS，Analysis，STAT 20 Introduction to Probability and Statistics，PROBABILITY AND STATISTICS, ECON 15A，Stat 134，Stat 151，ACTL 2131 Probability and Mathematical StatisticsACTL 5101 Probability and Statistics for Actuaries，37252 Regression and Linear Models，MATH STAT 302 Introduction to Probability，MATH 6420 - 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Physics(ASOP)，PX2620 Quantum Mechanics and its Applications，PHYS1121 Physics 1A，PHYS 100 Introductory Physics，PHYS2130 PHYSICS A，Physics 1112，Physics 1114，MATH0025 Mathematics For General Relativity，SEHH1049 Physics I，PHAS0038 - Electromagnetic Theory，PHAS0041-Solid State Physics，PHAS0042 Quantum Mechanics，PHY132 Introduction to Physics II，PHYS 102 D100 PHYSICS FOR THE LIFE SCIENCES II，PHY1001 Mechanics，PX275 Mathematical Methods，PX265-7.5 Thermal Physics II，PHYS96010 Compuational Physics，PHYS 2040 - RELATIVITY AND MODERN PHYSICS，PHYS 301605 Partial Differential Equations EXAM 1，PX145 PHYSICS FOUNDATIONS，PX1200 Electricity and Magnetism，PHAS0010 Classical Mechanics，Engineering Electromagnetics ELEC ENG 3103，PHY2049 Calculus-based Physics II，68201 Physics in Action，Physics 115a，Pyhsics 9B，Physics 141A，Physics 1201，Physics 1221，Physics 221，Physics 521，Physics 5C，PHYS 304，Physics 10004，Physics 8B，，Physics 1C，Physics 9A，Physics 1A…… 化学类：The Avogadro Exam，Canadian Chemistry Contest，CHEM 40A - 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best-online-courses · 2 years ago

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A Historical Journey of Data Analytics and the Modern Lens of Online Data Analytics Courses

The story of data analytics is an intricate tapestry woven across centuries, culminating in the vibrant landscape we navigate today. This article embarks on a historical journey, tracing the evolution of data analytics from its nascent roots to the digital age. Alongside this exploration, we'll illuminate the transformative role that online data analytics course play in reshaping the narrative and preparing professionals for the complexities of modern data analysis.

1. Early Beginnings: Statistical Foundations

The roots of data analytics can be traced back to the 17th century with the inception of statistics. Pioneers like John Graunt and William Sealy Gosset laid the groundwork for understanding populations and making inferences. The advent of probability theory in the 18th century by luminaries such as Pierre-Simon Laplace provided a statistical lens through which data could be interpreted, marking the early stages of what would later become data analytics.

2. The Rise of Computers: Emergence of Digital Analytics

The mid-20th century witnessed a paradigm shift with the advent of computers. Pioneers like Grace Hopper and John W. Tukey were instrumental in developing algorithms and statistical methodologies that paved the way for digital analytics. The transition from manual calculations to computer-assisted analysis marked a turning point, making data processing faster and more efficient.

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In the 1960s and 1970s, the concept of Business Intelligence (BI) emerged, focusing on the use of data to drive business decisions. Decision Support Systems (DSS) became prominent, integrating data analysis tools to support managerial decision-making. This era laid the groundwork for the integration of analytics into business processes, setting the stage for the data-driven culture we witness today.

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The late 20th century and early 21st century witnessed an unprecedented surge in data generation, marking the era of Big Data. The digital revolution, coupled with the proliferation of the internet, led to an explosion of data sources. Traditional methods of data analysis became insufficient, giving rise to the need for advanced techniques. Online data analytics courses emerged as a response to this demand, providing professionals with the skills to navigate the intricacies of Big Data analytics.

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engineeringexamssuck · 2 years ago

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Numbers in math?

what is that? all my math has letters in it.

only numbers I see are exponents (sometimes)

I remember when a letter in math was an issue

how naive I was back then

now I have to deal with quadruple integrals, Laplace transform, Euler's rule, and derivatives of displacement to get speed and acceleration.

at least the derivatives are easy

#math #no numbers #only letters #what is this #high school me really thought that I would never use Pythagoras theorem after graduating #that bitch is everywhere

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celestie0 · 1 year ago

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can i just first say this is sincerely one of the best things thats ever happened to me in my time on this app 🤣 tysm for this, i was hoping an actual engineer and/or physicist would find this post and im so enthralled rn

I am coming in here as a Professional Engineer who works with fluid flow all day and won't be distracted by imagining Gojo's girthy, throbbing member pulsing inside me as I feel his warm... What was I saying?

i literally screamed at this lmfao thx for matching the humor in ur peer review i cld cry

I DIDNT EVEN REALIZE UNTIL RN THAT L ISNT SUPPOSED TO BE LENGTH OF VAGINAL CANAL ITS JUST SUPPOSED TO BE FROM HIS URETHRA omg i gasped. i feel like how i used to feel leaving lecture halls in college thinking i slayed tf outta my physics exams n then the score comes back 44%🧍🏻‍♀️🤣 also tyvm for drawing over my diagram i am so greatly honored by this

omggg p1 is also supposed to be pressure at urethra n not vaginal entrance bc thats where the fluid is cumming from🧍🏻‍♀️………..this is why i stuck to bio LMAO im so humbled rn 🤣🤣 also godbless articles w the value in the title 🙇🏻‍♀️

engineer reblog op, are u insinuating that gojo uses his infinity to block cervix bruising action LMFAOOO 🤣🤣 i seriously can’t w this rn (also thats a pretty dope form of birth control)

i’m a little lost on the explanation regarding his intrusion of the vagina canal 🤔 i had to draw it to understand i think this is what you mean:

i just tried to look up what a laplace transform is n saw the integral n felt like crying🧍🏻‍♀️but i was curious ab it n why you said it’s applicable here and hmm are u referring to how gojo’s infinity does not act as an actual physical barrier as gege has stated in jjk, therefore there is no true “length” we can approximate here if he uses his infinity? i notice in this article that explains how there is this Se^-a0t aspect:

(i havent taken calculus in over four yrs if im so wrong ab this pls excuse me lmaooo) but is this part of the equation related to t (as some variable in a function based on the context?) as it approaches infinity (aka in this case his thrusts as he approaches his infinity barrier within this vagina canal)? idk what the actual correct variable is to assign for t haha or if that’s even something to assign here

but in the case mentioned in that article with t approaching infinity, plugging that in would look like this i believe:

and then graphed:

again i’ve absolutely no fucking clue if any of this is right 🤣 BUT IF THIS IS WHAT YOU MEANT FOR USE OF THAT LAPLACE TRANSFORM THING THEN…….😨 i am so mind boggled by this. beyond simple use of infinity to restrict impregnation/cervical injury within the vaginal canal, i am so intrigued by the math behind his infinity technique in general!!! i also wonder, he mentions that people get slower as they get closer to him, might that imply the y-axis is some unit of distance? since as x approaches infinity and y approaches this bound value dashed line (lol i think there’s a name for it i cant remember rn tho) the values of y become increasingly smaller which would match what gojo stated 🤔 again i’m so fearful i’m talkin out my ass rn i feel so vulnerable 🤣 i was a bio/biochem major so i didn’t take much maths/physics but i’m very intrigued by this rn. also dont know if this is what u were referring to in the first place either lmao

Tragically, this leaves a whole 1.25" of your sex un-railed, but you'll live in the modern sense and die in the Victorian Poetry sense.

I CANT BELIEVE I GET TO READ THIS REBLOG FOR FREE LMFAO

also you’re tellin me the ideal lovemaking bpm matches the ideal bpm for cpr? 😭 so i can save someone’s life to “stayin alive” by the bee gees but i can also rock someone’s world to it too?

haha 5% as in for significance? (im so haunted by p values thats all that came to mind) BUT OK IM ALL ONBOARD W NEGLECTING STUFF

ouuu thank u for bringing up the linear speed to cross sectional area stuff i was rly confused ab that haha but also i think the reason i turned it into volume was i just made the wild assumption that it takes him one minute to cum 🤣 so mls per min -> how much he cums but thats a stretch n also doesn’t make much sense biologically either for a lot of reasons lol

YAAAAY OUR WOMBS ARE COMPLIANT WITH OHIO STATE ENGINEERING STANDARDS 👏🏼 GIVE IT UP FOR MOTHER NATURE

ok this is way too fucking long, i just wanted to dump my thoughts, pls do not feel as though u need to respond to this, dear engineer reblog op. you’ve made my entire week regardless.

also, to answer quinny’s question here

@quinnyundertow

i think possibly “putputput” is most correct.

ALR PEACE OUT ✌🏼

- ellie professionalgojobrainrotloser42069

what is the flow rate of gojo’s sperm? 🤔

😈 😈 😈 ALRIGHT LET’S FIND OUT

shoutout to m00tie @quinnyundertow since u said there's nothing that turns you on more than hearing how mobile a man's flagella are. this one's for you bb.

alright, first off, because his cum is confirmed to be both incompressible fluid as well as move with laminar flow, these attributes satisfy the conditions of pouiseulle’s law:

i had to do a little bit of research to determine if it was laminar or turbulent flow, and apparently sperm travels with both stokes & laminar flow, which is pretty interesting, and also moves in a sinusoidal propagating wave, likely due to the movements/shape of the flagella

note: microscopic sperm travel & ejaculate fluid travel are two very different things, but i can’t solve for anything microscopic here so we’re just gonna go for the ejaculate fluid only

anyways, to use pouiseulle’s law, let’s first determine our variables, and make sure we get the units right as well! always draw a diagram w all the variables:

now, let’s identify the variables:

1. radius (r) of tube -> this refers to the pipe/tube, therefore in this case, the vaginal canal. now since gojo has decided to creampie, we can assume that the radius of the vaginal canal will be equivalent to the radius of his girth as he is stretching you out. gege told me the diameter of his big fat schlong is approximately 3 inch girth, therefore the radius = 3/2 = 1.5 inches

2. ΔP refers to change in pressure gradient, in this case i’ve decided to have P1 as pressure at vaginal canal opening, and P2 as pressure at the end where the cervix is. therefore, ΔP = (P1 - P2) for the equation. i know you’ve got that gorilla grip coochie, esp when the world’s strongest sorcerer is fuckin you SENSELESS, but all things considered this is a very difficult parameter to measure, therefore i found this article to help out with this:

we’re going to assume “contraction pressure” (at the vaginal canal opening) is P1, due to gojo’s intrusion. and we’re going to assume “pressure at rest” is P2 at the end near the cervix (he’s pulled out a lil bit ok this makes things easier for me)

kPa are the units that we want for ΔP in this case, therefore it’s a simple calculation:

ΔP = P1 - P2 = 41.8 kPa - 26.8 kPa = 15 kPa

3. the last variable we need to account for here is L, which is the length of the PIPE HE’S LAYIN INSIDE OF YOU (jk it’s just length of ur coochie). now, i imagine this man is a generous lover, and he’s alr made you cum a few before he stuck it inside, so with arousal, the vaginal canal length has likely increased to about 5 inches (moreso 4.75in based on avg values in research but he stretched you in even more during the sexing!!) therefore L = 5 in

4. the other two values are just constants:

π = pi 3.1415 (imma just use pi function in calc)

η = this is viscosity of a fluid. based on this research article, the viscosity of human semen is approximately 9.35 cps. we want these units in kPa•s (remember that your units need to match the units of the other variables), so we need to use density of sperm (1.043 g/ml) to convert the factor (i just used chatgpt lol) but the conversion factor is pretty similar therefore we will just plug in something close to 9.35 kPa•s (true value is a little smaller)

ALRIGHT WONDERFUL! WE HAVE DETERMINED ALL OF OUR VARIABLES :) NOW WE JUST NEED TO PLUG IT INTO OUR EQUATION/DIAGRAM:

*note: mind the units! (shown in blue) there are lots of variations on how flow rate can be shown w the units, so u wanna be careful that they match

YAAAAY!! so the flow rate (Q) of gojo’s cum is approximately 0.63787 in^3/sec ☺️💕

use a quick converter online, and we can make it into liters per minute -> 0.02214 l/min. convert this to milliliters -> 22.14 mls

which means that, in one of gojo’s average cumshots, he cums 22.14 mls of ejaculate !!! :0 sheesh that’s a lot!!

but how does this value compare to other men? research varies, but on average, men ejaculate between 1-10mls per orgasm, therefore the world’s strongest sorcerer cums more than TWICE the worldwide average!!

and one final calculation shows us that when he finishes, it’s at about 0.369 mls per second :) that's fuckin fast!!!

thank you for cumming to my ted talk!! byee

alr ellie out ✌🏼😖 (i have sm brainrot)

#can i put this post on my resume #although i made many errors #i wld still like to brag that an actual engineer cranked the numbers #thank god i at least used the right equation? LOL #i think baha #that’s always half the battle #gojo satoru #jujutsu kaisen #jjk #physics

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