God of black technology

Chapter 61 Differentiation

Wang Yun glanced at Wang Qiuyang, and Wang Qiuyang looked at him and said, "I'll share the dormitory with Liu Yang." Rong Lei couldn't laugh or cry, was he really the extra one?Professor Wan nodded, "Okay, you can choose the dormitory yourself. I will give you a privilege, first come first served, you can choose the dormitory that you think is good."

As for the dormitory conditions, Wang Yun didn't have very good requirements, as long as it can live in, people can wash and take a bath, and it's not too cold when it's cold in spring like this.

"By the way, the national competition will start on April 15th. After the national competition, some of you will stay in the capital directly for a new round of training. Prepare for the IMO, so - you don't have much time." After Professor Wan finished speaking, he waved his hand, "It's up to you how to arrange it."

After all, Professor Wan left the dormitory.Several people looked at each other, and Liu Yang said, "Then let's choose the dormitory directly?"

"Hey." Looking at a row of dormitories, several of them had keys inserted, Wang Qiuyang was still thinking in his heart, isn't he afraid of being stolen?

However, when he opened the door of the dormitory, he realized that he was not afraid of being stolen, there was simply nothing to steal.In the empty room, there were only two beds, quilts, and pillows.It couldn't be simpler, even if a thief wants to steal it, there is nothing to steal.

After opening all the five dormitories, Wang Yun directly chose the dormitory in the middle, while Wang Qiuyang and Rong Lei both chose the dormitory near Wang Yun.

Because it was a one-month training camp, Wang Yun brought quite a lot of clothes. When he put all the clothes in the closet, Wang Qiuyang was already standing outside the door and yelling, "Wang Yun, hurry up."

Yuan Chengde looked at Wang Yun while arranging his things and said, "Wang Yun, you seem to have a good relationship with your cousin."

"Almost." Wang Yun said with a smile, "It's been my psychological shadow since I was a child. I didn't physically transcend him, but I was kind-hearted."

Yuan Chengde couldn't help laughing when he heard Wang Yun's words, "So, in fact, your brother should thank you for not physically saving him?"

Wang Yun looked at Yuan Chengde with pursed lips and said, "Shouldn't he thank me?"

"What are you talking about?" Wang Qiuyang walked into the dormitory, "It's been a long time since I packed up, and it's almost noon, let's go to Professor Wan to get the meal card in the cafeteria."

"It will be ready soon." Wang Yun smiled at Yuan Chengde, and Yuan Chengde laughed so hard that he could hardly straighten his back.Wang Qiuyang asked very puzzled, "I'll go, what joke do you have so funny? Keep laughing, keep laughing... Really, it feels like you guys are hiding something from me."

"What can we hide from you?" Wang Yun raised his eyebrows, "I've already sorted it out, how about Yuan Shen?"

"I'm almost done too." Yuan Chengde stood up, "I'm going to wash my hands first, you wait a moment."

"I'll go, you say I've forgotten." Wang Yun scratched his head and followed Yuan Chengde to wash his hands together.He looked at Yuan Chengde with a playful smile and said, "How about it, is my brother so taller than that Gu Cheng that I don't know where he is?"

"Tsk." Yuan Chengde said while washing his hands, "Wang Yun, I'm afraid you are not a brother-in-law?"

"What the hell." Wang Yun said with a smile all over his face, "Didn't I want you to meet more people? Who would you say is better than Gu Cheng?"

"En." Yuan Chengde was silent for a while, "That's good, and he's pretty handsome, too bad he's straight."

emmmmm... when I didn't say anything.

When Wang Yun and Yuan Chengde reappeared, Wang Qiuyang frowned and said, "I'm going, why are you so slow?" Liu Yang next to him whispered, "Didn't you find out that there are only five of us so far? Where are the five people?"

"Yes." Rong Lei waited for his roommates all morning, but none of them appeared in front of him. It was time for dinner, and the roommates hadn't come yet.The other five people probably don't want to be super gods.

"Who knows?" Wang Yun shrugged his shoulders, "Maybe they have something to do." Wang Yun stretched his waist, he couldn't believe it, he hadn't read any books all morning. "Let's go to Professor Wan to get the meal card first, just to see what can be eaten at Yucheng University."

"I heard that our training camp was quite good this time. We ate in the staff canteen. Yucheng University has not yet started school, and there are not many students staying in school. Therefore, the student canteen is not open, only the staff canteen is open. We I have made a lot of money this time, and I heard that the staff canteen of Yucheng University is pretty good." Liu Yang spoke mysteriously as he walked.

Hearing Liu Yang talking like a treasure, Wang Yun took a look at Liu Yang, and said after a while, "Liu Yang, I really want to ask you a question."

Liu Yang froze for a moment, looked at Wang Yun and asked in confusion, "God Yun, what's your problem?"

"That's... that, um, did you tell the news about the exam?" Wang Yun glanced at Liu Yang, and Wang Qiuyang came back to his senses, "I mean, I never told anyone about this news, Why did everyone know about it, and it spread to Professor Wan's ears. Liu Yang, it turned out to be you."

Liu Yang has a relative who is a professor at Yucheng University, and he knows that these things are actually quite simple.

What Professor Wan told Wang Yun was that it was possible to take an exam, but he hadn't worked out the plan yet.After being told by Liu Yang, Professor Wan saw that they had spread so well, so he let them take the exam.Liu Yang almost cheated everyone in the training team, and everyone's eyes were on Liu Yang. Even Liu Yang had a thick skin and couldn't help making such a fuss, so he could only smile awkwardly and say, "I, actually I Didn't say anything, just...hehe."

"Who did you tell?" Wang Qiuyang was curious, who did this guy tell, and why the whole competitive circle is going crazy.

There are also some students from the first province who are waiting to fill their seats. Wang Qiuyang was curious. It is impossible for Wang Yun to talk about this matter when he sees people, and he has never said this matter before.

So how did this news get out? He ignored Liu Yang, the gossip prince——

"I just casually said something to my deskmate sitting next to me, who knew that he would tell everyone about it, so that everyone knew about it." Liu Yang scratched his head in embarrassment, and laughed awkwardly.He dug the pit. Although he didn't intend to trap his teammates, there is nothing wrong with him being a pit.

"You still don't know the personality of your deskmate?" Wang Qiuyang became confused, "You actually told him such an important matter, no wonder we were cheated by you, you cheater!"

After all, Wang Qiuyang's pace accelerated a lot, but fortunately, everyone was able to keep up with Wang Qiuyang's footsteps.When I came to the office of the number hospital, it was still very deserted.Professor Wan looked at the five people kindly, and asked casually, "Have the other students not come yet?"

"not yet."

"That's all right. I'll send you the meal cards first, and you can go to the staff cafeteria to eat." Professor Wan took out a few meal cards and put them on the table. The meal cards were printed with the teaching building of Yucheng University. with a name written on it.Professor Wan said, "One card per person, and everyone has a name. After you eat, go to classroom 4416. There is a number plate on the classroom. I believe you can find it. I will wait for you there."

After getting their meal cards, several people walked out of the office and said in a low voice, "What do you think Professor Wan told us to go directly to the classroom after eating?"

"I don't know, you can't let us take the exam?"

"Probably not, there are still a few people who haven't come yet." Speaking of this, Liu Yang paused, looked at Wang Qiuyang and asked, "Shen Wang, why don't you say they haven't come yet?"

"Who knows? Maybe there was a traffic jam in the morning." Wang Qiuyang shrugged his shoulders, "Besides, Professor Wan just said that he must report to the training team today, and he didn't say when he must arrive. Maybe they won't come until after class today.

"I'll go, isn't there only a few of us in the afternoon?"

"Isn't it good that there are only a few of us? Small class teaching, a dream come true."

After talking, they had already arrived at the cafeteria of Yucheng University.After lunch, they came to the teaching building of the School of Numbers, and after a while, they found classroom 4416.

Professor Wan sat on a chair and waited for them. When he saw them coming, he pointed to the empty classroom and said, "Sit whatever you want, you can only sit in the first row anyway."

"..." So what does it mean to sit casually?Everyone was covered with black lines. They sat in the first row. Professor Wan picked up the chalk and wrote the word 'calculus' on the blackboard.He turned around and said to them, "I believe everyone is familiar with it?"

Everyone nodded, and everyone had learned some calculus more or less.There are even monsters like Wang Yun and Yuan Chengde, who have basically learned calculus.Professor Wan put his hands on the podium and said with a smile, "Calculus is very useful for competitions. At this stage, I don't recommend you to study advanced or number theory. After all, there are still many contents in it that you still have to learn." I'm a little confused." Professor Wan smiled when he said this, "Of course, it doesn't include a monster who is studying analytic number theory and has time to take physics classes."

"Hey hey hey..."

"Ha ha……"

The atmosphere in the whole classroom suddenly relaxed, and Professor Wan continued while the iron was hot, "I originally planned to take the test this afternoon, but I didn't expect that there were still five people who didn't show up. Then let me tell you about calculus first, calculus It is mainly divided into differential calculus and integral calculus... Here, we have learned calculus very well. So far, I can see that Wang Yun is the only one. But don't be discouraged, everyone, your basic knowledge of mathematics is already very solid. Being able to stand out from tens of thousands of high school students, do you think you can't even learn a single calculus?"

"First, let's explain differentiation."

"Differentiation's definition in mathematics: From the function B=f(A), two sets of numbers A and B are obtained. When dx is close to itself in A, the limit of the function at dx is called the function at dx. differential." Professor Wan looked at the five students and said, "I mean, do you think it's quite simple?"

Several students nodded slightly, and Professor Wan continued, "This is just the basic concept of differentiation, and what I'm going to talk about next is monadic."

[Assume that the function y=f(x) is defined in the neighborhood of x, and x and x+Δx are in this interval.If the increment of the function Δy=f(x+Δx)-f(x) can be expressed as Δy=AΔx+o(Δx), and o(Δx) is an infinitesimal higher order than Δx, then the function f(x) is called in The point x is differentiable, and AΔx is called the differential of the function corresponding to the dependent variable increment Δy at the point x, denoted as dy, that is, dy=AΔx. 】

[The increment Δx of the independent variable x is called the differential of the independent variable, denoted as dx, that is, dx=Δx.So the differential of the function y=f(x) can be written as dy=f'(x)dx. 】

[When the independent variable X is changed to X+△X, the corresponding function value is changed from f(X) to f(X+△X), if there is a constant A that has nothing to do with △X, so that f(X+△X)-f The difference between (X) and A?△X is △X→0 about the high-order infinitesimal quantity of △X, then A?△X is the differential of f(X) in X, denoted as dy, and called f(X) Differentiable in X.In unary calculus, differentiable and differentiable are equivalent.Record A?△X=dy, then dy=f'(X)dX. 】

【For example: d(sinX)=cosXdX】

"Now?" Professor Wan wrote the formula on the blackboard while looking at the expression below.Seeing that everyone's face is not too bad, so he turned around, put the chalk on the podium and said, "I know, everyone should know something about differential. Then—"

Professor Wan picked up the chalk and wrote a topic on the blackboard——

【Find the differential dy of the function y=y(x) determined by the equation 2y-x=(x-y)ln(x-y)】

"???" Everyone was stunned at this moment. They read the calculus in a hurry. They could barely understand the basic knowledge that Professor Wan said just now. Forced.

Professor Wan smiled and said, "Why, no one volunteered to do it?"

Yuan Chengde glanced at Wang Yun, he was a little eager to try.However, Professor Wan smiled directly and said, "Well, since no one came up, then Wang Yun, you can come up and do it. If you do this question correctly, you can go back to rest this afternoon, or you can study in the classroom. Your analytic number theory or physics.

If there is such a good thing, why doesn't Wang Yun do it?

So he walked up to the blackboard, glanced at the topic, and wrote on the blackboard with chalk——

[Solve the differential equation on both sides of the equation

d(2y-x)=ln(x-y)d(x-y)-(x-y)dln(x-y)

2dy-dx=ln(x-y)(dx-dy)-(dx-dy) solves dy

There is dy=x/(2x-y)dx]

This question is actually very simple. If you think about it, you can solve it.It's just that they seem to be a little bit embarrassed about the differential calculation, which made Wang Yun take advantage of it.If Professor Wan hadn't directly named Wang Yun and asked him to come up and write the answer, I'm afraid Yuan Chengde would come up to the podium to do this question next.

Professor Wan looked at Wang Yun with a smile and nodded, "Go down."

When Wang Yun walked down, Rong Lei said with a fanciful expression on his face, "I'll go, Yunshen, this is too amazing."

Scratching his head, Wang Yun smiled and said, "Small meaning, small meaning."

"Okay, next, let's think about this topic." Professor Wan wrote other topics on the blackboard, and the other three people were crying and howling. They thought that they would relax a little before the other five people came. The professor has already started teaching them.

"Stop howling." Professor Wan put the chalk on the podium after finishing writing the question. "You can just solve this question this afternoon. As for the only one who answered correctly, Wang Yun, you can do whatever you like."

Only then did Wang Yun come up with analytic number theory, and he was always ready to ask Professor Wan.When putting the book on Professor Wan's podium, Professor Wan said with a smile, "Okay, you are really tricky in studying, and you are waiting for me here." When he said this, Professor Wan glanced at Wang Yun, " You want to see me stumble, right?"

Wang Yun hastily stopped and said, "I can't watch you stumble, Professor." He pointed to the content in the book and said, "It's about the problem of twin prime numbers. I'm a little unclear. Look—can you help me solve it? one time?"

"Of course." After taking a look at Wang Yun, Professor Wan studied the topic carefully, and then took the draft paper and calculated for Wang Yun on the paper.

The people below looked at Professor Wan and Wang Yun on the podium. Wang Yun nodded from time to time, and Professor Wan's mouth was full of words that he didn't understand.The god of learning is indeed worthy of being a god of learning, so it's better not to compare yourself with a scumbag like yourself, right?Comparing people to people makes people mad.

"Understood?" Standing on the podium for almost two hours, this question was finally solved by Professor Wan, and then Professor Wan said with a smile, "Keep reading, and you can ask me any questions you don't understand." .”

"Okay." Wang Yun happily walked off the podium with the draft paper and textbooks, and returned to his seat.Yuan Chengde said hastily, "Professor Wan, I have already finished this question, look..."

Professor Wan nodded, "Bring up your homework, and I'll see how you're doing." After a pause, Professor Wan continued, "If you do it right, you, like Wang Yun, can also make your own. Something happened."

"Hey." Yuan Chengde hurriedly took up the homework and handed it to Professor Wan.

So, Professor Wan carefully looked at Yuan Chengde's homework.Wang Qiuyang made a face at Wang Yun, lowered his voice, and asked softly, "Wang Yun, Wang Yun—how to do this question?"

Wang Yun glanced at Wang Qiuyang, covered his face, and originally wanted to talk to Wang Qiuyang, but Professor Wan raised his head and said, "Do your own thing, don't ask others. I believe that you can all do the right thing. "

Wang Yun spread his hands, expressing his regret, not because he didn't help Wang Qiuyang, but because Professor Wan didn't allow it.

"Very good, you can do your own thing now." Professor Wan glanced at Yuan Chengde with a smile. He remembered that this little classmate should be called Yuan Chengde, right?Although he didn't solve the last question of the final, Pei Shu's theorem was correct, at least part of it was proved, and he was also a remarkable young genius.

Think about it, there are two young geniuses in Yucheng this year, and they won't be able to win the national one. Professor Wan thinks that he can find a piece of tofu and kill him.

The sky is getting darker and darker, and although it is spring, winter is still not completely over.The cold wind rustled.Wang Yun stretched his waist, and it was not Rong Lei but Liu Yang who was still working on the problem.

While working on the topic, he muttered, "Wait a minute, I will figure it out soon, there is still a while, only a while."

Wang Qiuyang supported his chin with his hands, and said dumbfoundedly, "Go ahead, no one is urging you."

Professor Wan turned the thermos cup with both hands, and his eyes seemed to be focused on the thermos cup.Suddenly he stood up and waved at Wang Yun. Wang Yun was stunned for a moment, walked to the podium, looked at Professor Wan and said, "Professor Wan, what do you want?"

"I'll play something fun for you." Professor Wan picked up the paper and pen and wrote on the draft paper——

[For any odd natural number p, if two of the following statements are true, the remaining one will be true:

1.p=(2^k)±1或p=(4^k)±3

2. (2^p)-1 is a prime number

3.[(2^p)+1]/3 is a prime number]

"???" Wang Yun looked at Professor Wan in bewilderment, he didn't quite understand, what the hell is this?

Professor Wan looked at Wang Yun and said, "How about it, isn't it a surprise?"

This is a surprise?It's scary, right? !Wang Yun wanted to complain about Professor Wan, what kind of thing he saw, and with his current knowledge, he probably couldn't figure it out.

This topic has already made him feel a little confused, Professor Wan continued, "How about it, are you interested in studying it in depth?"

In-depth research?It's not necessarily to solve him, if it's just research, maybe - I can really do it.

"Okay, I'll take a look." Wang Yun took the draft paper and walked off the podium. Wang Yun was thinking as he walked, but couldn't think of a clue.Professor Wan looked at Wang Yun's appearance and said with a smile, "Take your time, don't worry. This question is not so easy to solve."

Wang Qiuyang moved his head closer, looked at it and said, "Let me see what the problem is that makes our cloud gods so difficult."

There are not many topics, even very short.But the amount of information contained in it was too great. After a glance, he was about to collapse. "Fuck, what the hell is this?"

"I'm finally done." Liu Yang exhaled slowly, Professor Wan looked at the time and said, "It's already six o'clock, and this is where you are the slowest."

"Hey..." Liu Yang smirked, not knowing what to say.When he took the homework book to the podium, Professor Wan corrected it, nodded and said, "Yes, today's topic is a little easier, but everyone did it right anyway. Tonight, other professors will give it to you." Before you explain calculus, you can go to the cafeteria to eat, and then go back to the classroom to study by yourself. When the time comes, the teacher will come naturally."

Professor Wan walked out of the classroom, watching Professor Wan walk farther and farther, the whole teaching building seemed very quiet, only the sound of pattering footsteps kept moving.

"Ah..." Liu Yang said, clutching his chest, "I didn't expect that the first day of Yucheng University would be so unhappy."

Wang Qiuyang sighed, "Be content, my friend, I feel that it will become more and more difficult in the future. Today is just a differential, who knows what it will be tomorrow."

"No matter what tomorrow is, I'm already hungry, let's go eat first." Rong Lei raised his hand and said weakly.

"Yes, yes, let's go eat first." Wang Qiuyang also began to be hungry, so he walked out of the classroom together with Rong Lei and Liu Yang, looked back at the two of them and said, "What are you waiting for? Hurry up, don't you eat?" Positive, there is something wrong with my head."

Wang Yun glared at Wang Qiuyang, "You are the only one who has a problem, let's go, Yuan Chengde, let's go to eat first."

"It's okay." Yuan Chengde shook his head, "You guys go to eat first, I'll take a look, and go to eat later."

"Really not going?"

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