Euler's Formula

Although he thoroughly disbelieved it in his heart, out of a professor's dignity, Blythe still decided to look at the draft paper Li Mo handed over.

He just sat like that, placing the draft paper casually on his knees, and started reading it casually.

There are bound to be plenty of common-sense operational errors; I'll just find one, and that will be enough to make them leave.

Unexpectedly, the steps written in the first line of the equation were quite orderly.

Professor Bryce nodded slightly, which showed that Li Mo still attended classes properly on ordinary days.

Next came the integral expression for the Fourier coefficients.

It turned out to be written without any problems... You could even say it was very standard.

Hmm?

Professor Bryce raised the draft paper up a little bit; he felt that something wasn't right...

The feeling that something wasn't right intensified as he read further down.

Finally, Professor Bryce sat straight up all at once, couldn't help but grab the draft paper, and paced around the grand hall.

This was his personal habit.

Once he grew excited, he subconsciously liked to walk back and forth and rack up steps.

At the same time, this was accompanied by incoherent muttering to himself:

"Phase angle... a completely new variable is introduced here..."

"No, this expansion..."

"The series expansion of the natural exponential function... imaginary numbers are substituted here..."

"But where did the remainder term go?"

He stopped in his tracks and closed his eyes to do mental arithmetic.

After calculating for a few seconds, he lowered his head again, a trace of excitement gradually revealing itself in his gaze.

Then came quickened footsteps.

The old man strode forward vigorously, kicking away a large amount of draft paper scattered on the floor.

Wayne was dumbfounded. He moved half a step toward Anna and said, "Anna, is the professor alright? He looks to be in a very bad state."

Fixing her gaze on Professor Bryce, Anna said, "Don't rush yet, let's just watch. I have a feeling the professor might be overly excited."

Wayne expressed complete inability to understand. He muttered, "Even if Li Mo solved the problem, that's just a single problem. Even if the result is correct, is there any need to get this excited?"

Wayne thought the professor's reaction was already exaggerated enough.

He didn't expect an even more exaggerated one to come.

Professor Bryce suddenly dropped onto the floor, using both hands and feet to frantically scramble through the draft paper.

"The raw drafts..."

"Where are the raw observation data drafts for Mendel Port from the past three years!"

The professor began writhing on the floor like a deformed character.

Wayne finally couldn't watch any longer and said, "Professor, what are you looking for? I'll help you!"

Just as he finished speaking.

Professor Bryce found it.

He laid the tide record table flat on the floor, and placed Li Mo's draft paper right beside it, cross-verifying the two.

A few seconds later, Professor Bryce scrambled up using all fours, rushed over to the mahogany bookshelf against the wall, pulled out a book from inside, and flipped the pages with a rustling sound.

After checking the information in the book, he staggered back over to Li Mo.

"Li Mo! Come here!" Pulling him over to the draft paper, Professor Bryce asked, "What substitution did you use when handling the product of periodic functions? What is this thing? Explain it to me quickly!"

Li Mo said, "This is a simplification method, Professor. The calculation volume is very large when dealing with the integration of products of multiple trigonometric functions. To simplify the process, I introduced an imaginary unit to convert the sine and cosine functions into complex exponential functions with the natural base. In this way, trigonometric multiplication becomes exponential addition in the complex plane, and all integration processes are transformed into polynomial operations in algebra. After calculating the result, you only need to extract the real part, and that is the tide height and time you want."

Professor Bryce: "???"

After standing blankly for quite a while, he said, "Who taught you this?"

Li Mo: "I came up with it myself."

Using the mindset of complex analysis to solve real analysis problems had a resounding name on Earth: Euler's Formula.

Although this world was very similar to Earth, there were still many differences in details; for instance, Euler had never existed, and naturally no one had ever proposed this theorem.

Professor Bryce took successive deep breaths and muttered to himself.

"Complex plane... exponential addition... extract the real part..."

Suddenly, he opened his arms wide, raised his head, and said:

"Wonderful! Seeing this method, I feel like a filthy sewer rat that suddenly raised its head and saw the sun! Simply wonderful!"

Li Mo instantly froze awkwardly and said, "Professor, don't put it like that."

Paying no attention to Li Mo, Professor Bryce walked with stiff strides to the very center of the room and then lay straight down.

He covered his face with both hands.

Sobbing sounds gradually drifted out.

Soon, the sobs turned into uninhibited crying.

Anna hurried to give Wayne a look.

Wayne stepped forward immediately. Adjusting his vest, he desperately wanted to display gentlemanly demeanor to offer comfort.

Yet he also felt somewhat at a loss.

Looking left and right, Wayne finally picked up a few clean, extra-large drawing paper drafts and covered the professor's belly with them.

There was no helping it; he had to make sure the professor didn't catch a cold first.

Having done this, Wayne tentatively asked, "Professor, are you alright?"

Professor Bryce kept lying on the floor, crying.

After waiting for a moment, Wayne asked again, "Professor, do you need me to pour you a cup of black tea?"

Covering his face, his body trembling with sobs, the professor said vaguely, "Sorry, you guys should leave first... leave."

Wayne looked back at Anna.

Anna nodded.

Li Mo thereupon spoke up, "Professor, then we'll be leaving first."

With that, the three of them turned and walked out of the laboratory.

Leaving Professor Bryce lying alone on the floor, his tears flowing backward into his white hair, while his mouth kept muttering:

"I made it in time... I made it in time; the Autumn Equinox... the Autumn Equinox..."

He burst into another bout of crying, then propped himself up with both hands and staggered to his feet.

He had to take action and send this prediction result to the Empress at the fastest possible speed...

Outside the laboratory door.

Seeing the three of them emerge, the female assistant walked up to them with concern and asked, "How did it go?"

Li Mo scratched his head.

Recalling the scene of the professor crying on the floor with draft paper covering his stomach, he truly didn't know how to describe it.

He could only say, "The professor told us to leave first."

"Oh, oh." Nodding as if it were only natural, the female assistant comforted him, saying, "It's alright, Mr. Li Mo. The professor was already quite gentle this time. On many previous occasions, he directly chased people out without even letting them say more than a single sentence."

Li Mo nodded in agreement, "Mm-mm."

Anna added, "Please pay more attention to the professor's health; he seemed somewhat emotional."

Was he angered to that point? Thinking this in her heart, the female assistant then said, "Rest assured, I'll keep an eye on him."

Just as Li Mo was preparing to leave, the female assistant took another step forward, closed in on Li Mo, and whispered a hint: "Mr. Li Mo, the professor's problems are indeed very difficult, but if you can know what the problem is in advance and prepare early, there might still be a possibility of passing."

Li Mo blinked and replied, "Um... thank you."

With that, the three of them left the top floor.

Walking at the very front, Li Mo suddenly felt a bit fatigued.

His feet suddenly stumbled, and his center of gravity pitched forward.

Fortunately, Anna was quick-eyed and nimble; rushing forward to catch Li Mo in her arms, she anxiously asked, "How is it? Are you okay?"

Li Mo figured it must be because he had used the concentration state for too long; he was indeed extremely exhausted.

However, not wanting to make Anna worry so much, he joked, "I'm fine. Help me up, I can still study."

Hearing those words made Anna flare up in anger!

She said, "Wayne! Help me carry Li Mo back home together!"

Tucking his cane under his armpit immediately, Wayne said, "Received!"

Li Mo: "Anna, I..."

Cutting him off directly, Anna said, "Don't speak! Elbow! Going home!"

Having said that, Anna pulled Li Mo's arm to prop it over her shoulder and led him downstairs.

She silently calculated in her heart:

This couldn't go on; even if Li Mo went back, he would still study in secret.

At least for today, she had to sleep with him! Watch him closely and not let him stay up late reading anymore!