NOVEL SIMPLE Xueba starts with change
Chapter 104
Chapter 104
Shen Jing stood at the door of the library, wondering what he was thinking.
He didn't even notice that Chen Zhou was approaching.
Chen Zhou patted him lightly: "What are you thinking about? So engrossed in thinking?"
Shen Jing came back to his senses, turned his head and glanced at Chen Zhou: "Uh...it's nothing."
Yang Yiyi also took the initiative to say hello: "Hello senior."
Only then did Shen Jing notice the girl next to Chen Zhou, and he sighed again in his heart. Now he fully understands what it feels like to have someone else's child by his side.
Even though he thought so in his heart, Shen Jing replied politely: "Sister, hello, hello."
On the way back to the dormitory, Yang Yiyi asked some questions about her academic score.
It's a question, but it's actually Yang Yiyi's own curiosity. Most of her questions are about this theorem and the ins and outs of that proof.
Chen Zhou patiently helped her answer one by one.
Some Chen Zhou is not very sure, and there is an outstanding senior in the mathematics department by his side, so he can ask for advice.
It's just that most of the fish that slipped through the net that Chen Zhou couldn't answer, Shen Jing didn't know much about.
Shen Jing listened to it with a special taste, and when he saw Yang Yiyi looking at Chen Zhou, his feeling was even more sour.
Shen Jing just wanted to say, I also want such a girlfriend.
After finally getting to the dormitory area, Shen Jing hurriedly said hello and walked quickly towards his own dormitory.
After Chen Zhou sent Yang Yiyi downstairs to the dormitory, he also went back to the dormitory.
in the dormitory.
Li Li and the others were reading at the desk.
Seeing Chen Zhou coming back, Zhao Qiqi immediately greeted him, and quickly asked, "Brother, how are you doing?"
Chen Zhou looked at him and said, "I've asked for you. If you have time, we can have a friendship together. You can handle it yourself when the time comes."
"Nice!" Zhao Qiqi hurriedly helped Chen Zhou take off his backpack, let Chen Zhou sit on a chair to rest, and then gave him a shoulder squeeze.
Then he said to Li Li and Zhu Mingli: "Well, haven't you heard? The dormitory fellowship, this is not for me alone, everyone has a share! Two Li, quickly pour a glass of water for Brother Chen. Lao Zhu, hurry up and serve the snacks."
Hearing this, Li Li took Chen Zhou's glass and went to pour a glass of water.
Zhu Mingli took out a large bag of delicious food that he treasured.
"It's too polite for you to do this." Chen Zhou ate a piece of beef with some embarrassment, and drank his saliva.
"You're welcome, you're welcome. Then, Brother Chen, when will we have a friendship?" Zhao Qiqi asked.
All three looked at Chen Zhou expectantly.
Chen Zhou thought for a while and said, "It's almost the mid-term exam season, how about after the exam is over?"
Zhao Qiqi: "Yes, yes."
Zhu Mingli: "It's a good time. If you do well in the exam, everyone has fun. If you don't do well in the exam, everyone coaxes you to be happy. Chen Zhou will arrange it."
Li Li: "So, let's prepare for the midterm exam first."
Chen Zhou: "That's right."
When the dormitory finally quieted down, Chen Zhou borrowed Li Li's computer and started downloading the mission information sent by Wu Xiping.
After the download was complete, Chen Zhou decompressed the file and flipped through the information.
He received two questions, one of which was based on his own example, and Wu Xiping gave him a zero point question.
This is a problem of pure mathematical analysis solved by higher algebraic methods.
Correspondingly, another topic is to use the method of mathematical analysis to solve the problem of pure higher algebra.
It can be said that Wu Xiping assigned the task of this project very reasonably.
If you look at each person's task individually, it can be done independently as a small project.
This is also Wu Xiping's deliberate effort to cultivate Chen Zhou and Shen Jing's research capabilities.
Chen Zhou transcribed the two topics on the draft paper and prepared to study them.
The topics of these two questions are very simple, full of short and concise aesthetic feeling.
But to solve it, the difficulty is not small.
After all, it is one thing to say it, but it is another thing to actually do it and study it.
Chen Zhou turned the pen, thinking about the corresponding solution.
After thinking for a while, Chen Zhou picked up his pen and began to solve the problem.
"If f(x)≠0, then the conclusion is true"
". It can be proved that there are at least N+1 x1, x2, x3,.., xn+1∈(a, b), and x1<x2<x3<xn+1, so that f(xi)=0, (i= 1, 2, ., n+1)"
After writing this, Chen Zhou paused, he had a strange feeling.
But Chen Zhou couldn't tell what this feeling was.
摇了摇头，陈舟继续写到：“假设这样的点只有m个.则有x0→x1∫C’Xf(x)dx+x1→x2∫C’Xf(x)dx+++xm→xm+1∫C’Xf(x)dx=0”
"According to the median value theorem of integrals, there exists ξi(i=1, 2, ., m) such that."
"According to the arbitrariness of C, and the Vandermonde determinant is not equal to zero, we have"
"Therefore f(x)=0, contradicting f(x)≠0."
To solve this problem, Chen Zhou used his own ideas to connect mathematical analysis and advanced algebraic knowledge horizontally to solve the problem.
Chen Zhou looked at the steps he had written down, and used advanced algebra to solve the problem of pure mathematical analysis.
After sorting it out again, Chen Zhou felt that strange feeling again.
Is it because it is the first time to infiltrate and fuse different courses to solve the strange feeling generated by the problem?
After thinking for a while, Chen Zhou did not get a definite answer.
He raised his hand and looked at his watch. It was almost 12 o'clock, and Li Li and the others were still reading.
Chen Zhou got up to wash his face, then returned to the desk, and continued to read the next question.
The next question is to use the method of mathematical analysis to solve the problem of pure higher algebra.
A very typical topic, the title only has one sentence.
"Assume ai>0, and ai are all different, i=1, 2, ., n, prove: the square matrix A (1/(ai+aj)) is a positive definite matrix."
After Chen Zhou finished reading, he thought for a while, and he already had an idea.
The reason why this question is typical is that it requires the use of typical mathematical analysis methods, the generalized integral ∫+∞e^(-ax)dx=1/a(a≠0).
"First of all, it is a real symmetric matrix, and any x can be introduced into the integral for calculation."
Keep thinking, write like a god.
Chen Zhou kept moving his hand holding the pen, and wrote out his problem-solving process on the draft paper.
".Because a1, ., an are different from each other, if x1e^(-a1t)++xne^(-ant)=0, x1==xn=0, so they are contradictory."
After writing this, the answer basically came out.
Chen Zhou's strange feeling reappeared.
Chen Zhou ignored this feeling, and solved the whole problem according to the train of thought.
".Using the above conclusions, it can be proved that the matrix ...is positive definite."
The question itself was solved, but Chen Zhou's strange feeling did not find the answer.
Chen Zhou glanced at the time, only half an hour had passed, it was still early.
He put the scratch paper aside and planned to do the two questions again.
Mathematical analysis methods are used for fractional questions, and advanced algebra methods are used for advanced algebra questions.
Chen Zhou wanted to find the connection from the question, he thought the question would tell him the answer.
(End of this chapter)
Shen Jing stood at the door of the library, wondering what he was thinking.
He didn't even notice that Chen Zhou was approaching.
Chen Zhou patted him lightly: "What are you thinking about? So engrossed in thinking?"
Shen Jing came back to his senses, turned his head and glanced at Chen Zhou: "Uh...it's nothing."
Yang Yiyi also took the initiative to say hello: "Hello senior."
Only then did Shen Jing notice the girl next to Chen Zhou, and he sighed again in his heart. Now he fully understands what it feels like to have someone else's child by his side.
Even though he thought so in his heart, Shen Jing replied politely: "Sister, hello, hello."
On the way back to the dormitory, Yang Yiyi asked some questions about her academic score.
It's a question, but it's actually Yang Yiyi's own curiosity. Most of her questions are about this theorem and the ins and outs of that proof.
Chen Zhou patiently helped her answer one by one.
Some Chen Zhou is not very sure, and there is an outstanding senior in the mathematics department by his side, so he can ask for advice.
It's just that most of the fish that slipped through the net that Chen Zhou couldn't answer, Shen Jing didn't know much about.
Shen Jing listened to it with a special taste, and when he saw Yang Yiyi looking at Chen Zhou, his feeling was even more sour.
Shen Jing just wanted to say, I also want such a girlfriend.
After finally getting to the dormitory area, Shen Jing hurriedly said hello and walked quickly towards his own dormitory.
After Chen Zhou sent Yang Yiyi downstairs to the dormitory, he also went back to the dormitory.
in the dormitory.
Li Li and the others were reading at the desk.
Seeing Chen Zhou coming back, Zhao Qiqi immediately greeted him, and quickly asked, "Brother, how are you doing?"
Chen Zhou looked at him and said, "I've asked for you. If you have time, we can have a friendship together. You can handle it yourself when the time comes."
"Nice!" Zhao Qiqi hurriedly helped Chen Zhou take off his backpack, let Chen Zhou sit on a chair to rest, and then gave him a shoulder squeeze.
Then he said to Li Li and Zhu Mingli: "Well, haven't you heard? The dormitory fellowship, this is not for me alone, everyone has a share! Two Li, quickly pour a glass of water for Brother Chen. Lao Zhu, hurry up and serve the snacks."
Hearing this, Li Li took Chen Zhou's glass and went to pour a glass of water.
Zhu Mingli took out a large bag of delicious food that he treasured.
"It's too polite for you to do this." Chen Zhou ate a piece of beef with some embarrassment, and drank his saliva.
"You're welcome, you're welcome. Then, Brother Chen, when will we have a friendship?" Zhao Qiqi asked.
All three looked at Chen Zhou expectantly.
Chen Zhou thought for a while and said, "It's almost the mid-term exam season, how about after the exam is over?"
Zhao Qiqi: "Yes, yes."
Zhu Mingli: "It's a good time. If you do well in the exam, everyone has fun. If you don't do well in the exam, everyone coaxes you to be happy. Chen Zhou will arrange it."
Li Li: "So, let's prepare for the midterm exam first."
Chen Zhou: "That's right."
When the dormitory finally quieted down, Chen Zhou borrowed Li Li's computer and started downloading the mission information sent by Wu Xiping.
After the download was complete, Chen Zhou decompressed the file and flipped through the information.
He received two questions, one of which was based on his own example, and Wu Xiping gave him a zero point question.
This is a problem of pure mathematical analysis solved by higher algebraic methods.
Correspondingly, another topic is to use the method of mathematical analysis to solve the problem of pure higher algebra.
It can be said that Wu Xiping assigned the task of this project very reasonably.
If you look at each person's task individually, it can be done independently as a small project.
This is also Wu Xiping's deliberate effort to cultivate Chen Zhou and Shen Jing's research capabilities.
Chen Zhou transcribed the two topics on the draft paper and prepared to study them.
The topics of these two questions are very simple, full of short and concise aesthetic feeling.
But to solve it, the difficulty is not small.
After all, it is one thing to say it, but it is another thing to actually do it and study it.
Chen Zhou turned the pen, thinking about the corresponding solution.
After thinking for a while, Chen Zhou picked up his pen and began to solve the problem.
"If f(x)≠0, then the conclusion is true"
". It can be proved that there are at least N+1 x1, x2, x3,.., xn+1∈(a, b), and x1<x2<x3<xn+1, so that f(xi)=0, (i= 1, 2, ., n+1)"
After writing this, Chen Zhou paused, he had a strange feeling.
But Chen Zhou couldn't tell what this feeling was.
摇了摇头，陈舟继续写到：“假设这样的点只有m个.则有x0→x1∫C’Xf(x)dx+x1→x2∫C’Xf(x)dx+++xm→xm+1∫C’Xf(x)dx=0”
"According to the median value theorem of integrals, there exists ξi(i=1, 2, ., m) such that."
"According to the arbitrariness of C, and the Vandermonde determinant is not equal to zero, we have"
"Therefore f(x)=0, contradicting f(x)≠0."
To solve this problem, Chen Zhou used his own ideas to connect mathematical analysis and advanced algebraic knowledge horizontally to solve the problem.
Chen Zhou looked at the steps he had written down, and used advanced algebra to solve the problem of pure mathematical analysis.
After sorting it out again, Chen Zhou felt that strange feeling again.
Is it because it is the first time to infiltrate and fuse different courses to solve the strange feeling generated by the problem?
After thinking for a while, Chen Zhou did not get a definite answer.
He raised his hand and looked at his watch. It was almost 12 o'clock, and Li Li and the others were still reading.
Chen Zhou got up to wash his face, then returned to the desk, and continued to read the next question.
The next question is to use the method of mathematical analysis to solve the problem of pure higher algebra.
A very typical topic, the title only has one sentence.
"Assume ai>0, and ai are all different, i=1, 2, ., n, prove: the square matrix A (1/(ai+aj)) is a positive definite matrix."
After Chen Zhou finished reading, he thought for a while, and he already had an idea.
The reason why this question is typical is that it requires the use of typical mathematical analysis methods, the generalized integral ∫+∞e^(-ax)dx=1/a(a≠0).
"First of all, it is a real symmetric matrix, and any x can be introduced into the integral for calculation."
Keep thinking, write like a god.
Chen Zhou kept moving his hand holding the pen, and wrote out his problem-solving process on the draft paper.
".Because a1, ., an are different from each other, if x1e^(-a1t)++xne^(-ant)=0, x1==xn=0, so they are contradictory."
After writing this, the answer basically came out.
Chen Zhou's strange feeling reappeared.
Chen Zhou ignored this feeling, and solved the whole problem according to the train of thought.
".Using the above conclusions, it can be proved that the matrix ...is positive definite."
The question itself was solved, but Chen Zhou's strange feeling did not find the answer.
Chen Zhou glanced at the time, only half an hour had passed, it was still early.
He put the scratch paper aside and planned to do the two questions again.
Mathematical analysis methods are used for fractional questions, and advanced algebra methods are used for advanced algebra questions.
Chen Zhou wanted to find the connection from the question, he thought the question would tell him the answer.
(End of this chapter)
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