If you don't get a score in the exam, in Xu Chuan's opinion, that's something that only bastards do.

Every time he can get a score in an exam, he will do his best to get it.

After checking the questions, I put pen to paper.

Instead of using the conventional high school solution method, Xu Chuan started from the Dirichlet function and put D(X)=lim(k→∞){lim(j→∞)cos(k!) πx)²} turns to the university's Dirichlet integral and solves for it.

He didn't do these three problems in the usual way, because the nature of the Dirichlet function is quite peculiar, and its image is an even function with the Y axis as the axis of symmetry.

It is a constructive function in analysis, which has many special properties, such as it is discontinuous everywhere, the limit does not exist everywhere, and the non-Riemannian integral is not available.

This kind of function is generally used in mathematical analysis, real variable function and functional analysis, composite function and other fields, and is used to construct some counterexamples to judge the truth of some mathematical conjectures and mathematical propositions.

To solve this problem in the conventional way, the answers that need to be written will be very long, and the various formula changes are quite cumbersome.

However, if the Dirichlet function is transformed into a Dirichlet integral, and then the relevant knowledge of the remaining numbers in the complex variable function is used to solve the integral, and then the Laplace transform and the Fu integral are used to solve the problem.

In this way, the steps that would have required complex calculation methods have been simplified to three steps.

This solution is not actually something in the field of pure mathematics, strictly speaking, it is the knowledge in the equation of physical damping free vibration.

Using this method, it needs to be supported by a certain amount of university physics knowledge, which is a new knowledge he learned from "Advances in Physics" some time ago.

At that time, his first paper was published in the journal Progress in Physics, and while browsing his papers, Xu Chuan saw something very interesting by the way.

A paper on the equation of damped free vibration.

Later, he borrowed the journal from Old Tang, studied the paper carefully, and then thought about the solution of this transformation of the Dirichlet function, and prepared to write another paper.

I didn't expect it to be applied here now.

.......

The three-question function problem is not too difficult for Xu Chuan.

He has enough knowledge to make the complex solution steps of these functions extremely simple.

It didn't take fifteen minutes, it didn't take ten minutes, and in less than five minutes, he solved these three problems.

Collect the pen, check and confirm, and submit the paper directly after there is no problem.

Today, he has won the five extra bonus points, and Jesus can't stop it!

"You're done?"

On the podium, Zhang Weiping took the answer sheet from Xu Chuan's hand in disbelief, turned his head to look at the wall clock above the blackboard, and the bright hands told him that only five minutes had passed!

How is this possible?

Is this still a high school student?

He never imagined that a high school student would be able to solve these three function problems in just five minutes.

These questions are dismantled from encrypted messages, and although they have been split and degraded, they are not low.

He originally expected Xu Chuan to make it, but it took at least fifteen minutes or more.

But now in just five minutes, he's handed in the papers?

"Hmm."

Xu Chuan nodded, handed in the test paper, and returned to his seat.

Zhang Weiping took a deep breath of air and looked at the answer sheet.

Let him see what kind of answer this genius has given.

Seeing it, the black handwriting on the answer sheet was reflected in the pupils, and the answer, which did not occupy much space, made Zhang Weiping frown for the first time.

The answers to these three questions are very clear to him, and if the correct answers come out, the answers to each question will definitely occupy more than half a page of A4 paper.

But now he has the answer sheet in his hand, and the answer to each question is only a few lines.

"Did you do something wrong?"

An idea immediately came to Zhang Weiping's mind, but he still frowned and continued to read.

When the lines of formulas came into view, the slightly frowning brow remained the same, but the black pupils were rapidly shrinking.

The thermos cup in his hand was quickly put down, and he who was originally holding the answer sheet with one hand has now become a two-handed protector.

On the answer sheet, the lines of calculations quickly flowed into his mind, stealing all his attention.

By the time I had read all the answers to the first question, nearly ten minutes had passed.

For ten minutes, Zhang Weiping's eyes only contained the black handwriting and mathematical formulas on the white paper on his hand.

After carefully confirming that there were no questions on the answer sheet, Zhang Weiping stood up and called Xu Chuan to his dedicated office with a solemn face.

"Who taught you this solution?"

In the office, Zhang Weiping pinched the answer sheet in his hand and stared at Xu Chuan and asked.

"I researched it myself, but I haven't been proven yet, I don't know if it's right or wrong, and tonight's topic can be used in this way, so I gave it a try."

Xu Chuan replied that this is indeed what he has researched himself, but it has only been researched for a short time, and he has not had time to publish it.

"I'm serious, no kidding, your method of solving the problem is very important! If someone else taught you, be sure to tell me who it is. ”

Zhang Weiping frowned tightly and reiterated it in a serious tone.

"No one else, this is my own."

Xu Chuan shook his head and confirmed again.

Hearing this, Zhang Weiping's pupils shrank, turned around and opened a black box in the office, took out a stack of cardboard from it, picked one out, and handed it to Xu Chuan.

"Do this, make this problem!"

"Don't ask why, if you can do it, I'll explain it to you later."

Xu Chuan took the card with some confusion and looked at it.

On the card, there is a question.

To be precise, it is a mathematical law problem, a mathematical law problem about Dirichlet function, and the logical calculation in it contains some decimal transcoding rules, which is very interesting.

"That's what we just did about the problem that was removed from this?"

After reading the question, Xu Chuan raised his head and asked, he saw the shadow of the three questions he had just done from this question.

"Can you make it?"

Zhang Weiping didn't answer, but asked rhetorically.

.....