Chapter 41: Doing Questions (Additional update after investing 100 yuan, third update please vote for follow-up reading)
Not getting points in the exam, in Xu Chuan's opinion, was 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 conventional high school problem-solving methods, Xu Chuan started from the Dirichlet function and turned D(X)=lim(k→∞){lim(j→∞)cos(k!πx)} to the university’s Dirichlet function
Integrate and then solve.
He did not use conventional methods to solve these three questions because the properties of the Dirichlet function are quite special. Its graph has the Y-axis as the symmetry axis and is an even function.
It is a constructive function in analysis and has many special properties, such as it is discontinuous everywhere, has no limit everywhere, cannot be Riemannian integral, etc.
This kind of function is generally used in mathematical analysis, real variable function and functional analysis, composite functions and other fields. It is used to construct some counterexamples to judge the authenticity of some mathematical conjectures and mathematical propositions.
If you use conventional methods to solve this problem, the answer you need to write will be very long, and the various formula changes are quite troublesome.
But if the Dirichlet function is converted 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 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.
On the podium, Zhang Weiping took the answer sheet from Xu Chuan in disbelief and turned to look at the wall clock above the blackboard. The bright hands told him that only five minutes had passed!
"You're done?"
"Don't ask why, if you can do it, I will explain it to you later."
In the office, Zhang Weiping held the answer sheet in his hand and stared at Xu Chuan and asked.
He originally expected Xu Chuan to be able to do it, but it would take at least fifteen minutes.
At that time, his first paper was published in the journal "Progress in Physics". While browsing his paper, Xu Chuan saw something very interesting.
"Did you do something wrong?"
But now, in just five minutes, he handed in the paper?
A paper on the equations of damped free vibration.
After reading all the answers to the first question, nearly ten minutes had passed.
Zhang Weiping frowned and reiterated in a serious tone.
Using this method requires a certain amount of university physics knowledge to support it, which is new knowledge he learned from "Progress in Physics" some time ago.
On the card is a question.
Upon entering his eyes, the black handwriting on the answer sheet was reflected in his pupils. The answer, which occupied only a small space on the page, immediately made Zhang Weiping frown.
"I'm serious, I'm not kidding. Your problem-solving method is very important! If someone else taught you, please tell me who it is."
Xu Chuan nodded, handed in the test paper and returned to his seat.
"Do this, complete this question!"
An idea came to Zhang Weiping's mind for the first time, but he still frowned and continued reading.
Xu Chuan replied that this was indeed something he had researched by himself, but he had only researched it a short time ago and had not yet had time to publish it.
Zhang Weiping took a deep breath of air and looked at the answer sheet.
How can this be?
He was determined to get the five extra bonus points today, and Jesus couldn’t stop him!
These questions are disassembled from encrypted messages. Although they have been dissected and degraded, they are still very difficult.
Later, he borrowed the journal from Lao Tang, studied the paper carefully, and then thought about the problem-solving idea of transforming the Dirichlet function, and prepared to write another paper.
It didn't take fifteen minutes, nor ten minutes. He solved these three questions in less than five minutes.
Let him see what kind of answer this genius gave.
He knew the answers to these three questions very well. If answered correctly, the answer to each question would definitely occupy more than half an A4 page.
Xu Chuan took the card with some confusion and looked over it.
During these ten minutes, Zhang Weiping could only see the black writing and mathematical formulas on the white paper in his hand.
Collect the pen, check and confirm, and hand it in directly if there are no problems.
"No one else, this is my own."
He has enough knowledge to transform the complex solution steps of these functions into extremely simple ones.
Xu Chuan shook his head and confirmed again.
"Um."
I didn't expect it could be applied here right now.
"I researched it myself, but I haven't gotten the proof yet, so I don't know whether it's right or wrong. This method can be used for tonight's question, so I gave it a try."
This solution is actually not something in the field of pure mathematics. Strictly speaking, it is knowledge in the damped free vibration equation of physics.
After carefully confirming that all the answers on the answer sheet were completely correct, Zhang Weiping stood up and called Xu Chuan into his dedicated office with a solemn expression.
To be precise, it is a mathematical rule question about the Dirichlet function. The logical calculations in it include some base transcoding rules, which is very interesting.
"Who taught you this solution?"
On the answer sheet, the rows of calculations quickly flowed into his mind, taking away all his attention.
But now the answer sheet in his hand has only a few lines of answers to each question.
When the rows of formulas came into his eyes, the slight frown remained unchanged, but the black pupils narrowed rapidly.
He quickly put down the thermos cup in his hand, and he who originally held the answer sheet with one hand now had two hands protecting it.
Hearing this, Zhang Weiping's pupils shrank, he turned around and opened a black box in the office, took out a stack of cardboard, picked one, and handed it to Xu Chuan.
The three function questions were not too difficult for Xu Chuan.
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.
"The question we just did was taken from this?"
After reading the questions, Xu Chuan raised his head and asked. He saw the shadow of the three questions he just did in this question.
"Can it be made?"
Zhang Weiping did not answer, but asked a question.