Great Country Academician

In Xu Chuan's view, not getting points in the exam is something only a bastard would do.

He will do his best to get the points he can get in every exam.

After checking the topic, I started writing.

Instead of using the conventional high school problem-solving method, Xu Chuan started from the Dirichlet function and turned D(X)=lim(k→∞){lim(j→∞)cos(k!πx)} to the Dirichlet function of the university Integrate and then solve.

He did not use conventional methods to solve these three problems, because the nature of the Dirichlet function is quite special, its graph is symmetrical with the Y axis, and it is an even function.

It is a constructive function in analysis and has many special properties, such as discontinuity everywhere, no limit everywhere, no Riemann integration, etc.

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

To solve this problem in a conventional way, the answer to be written will be very long, and various formula changes are quite troublesome.

But if the Dirichlet function is transformed into a Dirichlet integral, and then the relevant knowledge of the residue in the complex variable function is used to solve the integral, and then the Laplace transform and the Fourier integral are used to solve the problem.

In this way, the steps that originally required complex calculation methods were directly simplified to three steps.

This kind of solution is actually not something in the field of pure mathematics. Strictly speaking, it is the knowledge in the damped free vibration equation of physics.

Using this method requires a certain amount of university physics knowledge to support it, which is the new knowledge he learned from "Progress in Physics" some time ago.

At that time, his first paper was published in the journal Advances in Physics. When browsing his paper, Xu Chuan saw some interesting things by the way.

A paper on the damped free vibration equation.

Later, he borrowed the journal from Old Tang, studied the paper carefully, and then thought about the problem-solving idea of ​​transforming the Dirichlet function, and planned to write another paper.

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

The three function questions were not too difficult for Xu Chuan.

He has enough knowledge to transform the complex solution steps of these functions into extreme simplicity.

It didn't take fifteen minutes or ten minutes. In less than five minutes, he solved these three problems.

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

He has decided on the five bonus points today, and Jesus can't stop him!

"You're done with it?"

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

How can this be?

Is this still a high school student?

He never thought that a high school student could solve these three function problems in just five minutes.

These questions were disassembled from the encrypted message. Although they have been disassembled and degraded, the difficulty is not low.

He originally expected that Xu Chuan could make it, but it took at least fifteen minutes.

But now, in just five minutes, he handed in the paper?

"Um."

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

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

Let him see what kind of answer this genius gave.

After entering the eyes, the black handwriting on the answer sheet was reflected in the pupils, and Zhang Weiping frowned at the first answer that occupied a small space.

He knew the answers to these three questions very well. If they were answered correctly, the answers to each question would definitely occupy more than half a page of A4 paper.

But now the answer sheet in his hand has only a few lines of answers for each question.

"Did you do something wrong?"

An idea immediately came to Zhang Weiping's mind, but he continued to read with a frown.

When the lines of formulas came into his eyes, the slightly wrinkled brow remained unchanged, but the black pupils shrank rapidly.

The thermos cup in his hand was quickly put down, and he who was holding the answer sheet with one hand now became two hands to protect it together.

On the answer sheet, the lines of calculations quickly flowed into his mind, taking all his eyes away.

After reading all the answers to the first question, nearly ten minutes had passed.

During these ten minutes, Zhang Weiping only saw the black writing and mathematical formulas on the clean white paper in his hands.

After earnestly confirming that none of the answers on the answer sheet were completely correct, Zhang Weiping stood up and called Xu Chuan to an office dedicated to him with a solemn face.

"Who taught you this solution?"

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

"I researched it myself, but it hasn't been proven yet, so I don't know if it's right or wrong. Tonight's topic just happens to be applicable to this method, so I tried it."

Xu Chuan replied that this was indeed something he had researched by himself, but it was only a short time ago and he had not had time to publish it.

"I'm serious, I'm not kidding, your problem-solving method is very important! If someone taught you, please tell me who it is."

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

"No one else, this is mine."

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 inside, picked out one, and handed it to Xu Chuan.

"Do this, make this topic!"

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

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

On the card is a question.

To be precise, it is a question about mathematical laws, about the mathematical laws of Dirichlet functions. The logical calculations in it include some rules of base transcoding, which is very interesting.

"The topic we just did was removed from this?"

After reading the question, Xu Chuan raised his head and asked a question. From this question, he saw the shadow of the three questions he just did.

"Can it be done?"

Zhang Weiping didn't answer, but asked a question instead.