The world of mathematics is really interesting, and Yu Hua learns it with gusto. After understanding the story of calculus, he completely understands the definition of modern limits.
The limits successively perfected and redefined by Cauchy, the 'founder of calculus', and Weierstrass, the father of modern analysis, are the basis of calculus.
Cauchy limit definition - when the successive values of a variable approach a fixed value infinitely, if the difference between it and the fixed value can be arbitrarily small, then the fixed value is called its limit. .
The limit defined by Cauchy is very interesting. Although there are still factors such as geometry, motion and intuitive understanding, it avoids the fatal flaw of Leibniz's infinitesimal quantities.
It can be as small as you like, which means I will be as small as you want me to be. I won’t go to you. As long as you say a number, I will immediately become that number. If you ask me to become infinitesimal, then Tell us what infinitesimal is. Anyway, there is always a value that is the limit value.
In the hands of Weierstrass, the father of modern analysis, the limit definition of this passage was completely described in mathematical language - if and only if for any ε, there is a δ0, such that as long as 0|xa| δ, there is |f(x)-L|ε, then the limit of f(x) at point a is L.
The mathematical symbol for limit is denoted lim.
"Limits are unique and bounded..." Hua Luogeng saw that Yu Hua sounded unstressed, and the lecture speed became faster and faster, quickly passing over the definition and properties of limits, and then explained the function limits in detail.
Limits of functions is a course for first-year students at the University of Cambridge abroad. It includes infinitesimals and infinities, limits of functions and limits of sequences, limit operation rules and two important limits, etc.
Yu Hua silently absorbed the content explained by Hua Luogeng. All kinds of obscure mathematical knowledge in his mind gradually integrated and completely transformed into something of his own. It has to be said that teaching by famous teachers and self-study are completely different concepts. The learning and absorption efficiency of the former is Many times the latter.
Time passed slowly, about two hours later.
"Okay, today's class is here for the time being. When I go back, I will write an article about Cauchy's inequality as homework. Are there any questions?" Hua Luogeng looked at the time and chose to end today's class. He turned to Yu Hua and arranged road.
Is this how to write an article?
Yu Hua was slightly surprised. The article Hua Luogeng said was not a copy of the question, but an article about understanding Cauchy's inequality. It was similar to the nature of a paper. It was really unexpected that such an 'assignment' was assigned in the first class.
The two-hour course covered everything from extremes to the introduction to integral calculus. Yu Hua learned quickly, and Hua Luogeng naturally taught quickly as well.
"Okay, no problem." Yu Hua nodded, stood up and bowed to Hua Luogeng and saluted: "Thank you, Professor."
Cauchy's inequality is one of the contents of integral calculus. It is easy to understand and not too difficult.
Glancing at Yu Hua, Hua Luogeng smiled slightly: "Be careful on the way back."
"Student understands." Yu Hua nodded.
…
The sun is shining brightly, and the thick snow in the Tsinghua University campus reflects the light.
There was a new schoolbag hanging on his body, which contained four important English-original high-mathematics textbooks. The schoolbag was a gift from his wife Wu Xiaoyuan. With some time left, he was going to do something to settle the final payment and the collection of questions for Huangchenggen Bookstore.
The west courtyard is basically a single-family courtyard, surrounded by white snow. When Yu Hua walked halfway to the buildings in the west courtyard, suddenly, the door marked No. 11 on the right opened.
"Squeak!" A slight friction sound came out.
Immediately afterwards, a young man wearing a student uniform came out, his face was reddish, and he looked like he was sick.
"Ah!" The next second, the boy couldn't help but sneeze.
Looking at this handsome boy, Yu Hua smiled and nodded.
The young man was startled for a moment. It was the first time he saw a strange young man in the West Courtyard at this time. When he saw Yu Hua's smile, he smiled subconsciously.
Yu Hua's smile did not diminish and he walked towards the entrance of the west courtyard.
"Zhen Ning, do you have any questions?" At this time, a middle-aged woman wearing a winter coat came out and came to the boy's side, asking with concern.
"It's okay. I'm much better after taking medicine. Mother, who is that young man?" The young man Yang Zhenning shook his head gently. Yesterday he had a cold and fever at school. Mr. Ren immediately sent him back to Tsinghua University. He took two pairs of Chinese medicine. Today, Feeling more comfortable, Yang Zhenning looked at Yu Hua who was gradually going away, and said to his mother Luo Menghua.
Luo Menghua glanced at Yu Hua's back. He was very unfamiliar and shook his head gently: "I don't know, maybe you are a student in the school. Would you like to rest again? Sir, I have asked you to take two days off."
"No, Zhen Ning is much better now. Studies are very important and we can't delay for a moment. Jiaxian is still waiting for me at school."
The young man Yang Zhenning shook his head repeatedly. He couldn't stand the life of staying at home. He was about to enter the second grade and his studies were quite tight: "Goodbye, mother, you go back, don't catch a cold."
"Well, be sure to pay attention to safety on the road." Hearing the concern from his son, Luo Menghua smiled tenderly, his eyes full of love.
"From Zhenning Province." The young man smiled.
…
Yu Hua walked out of the quiet and peaceful Tsinghua Garden, hailed a rickshaw, and went straight to Jinguo Hutong in Ping'anli to go home first. Xu Rui and Xu Erya were very excited to see Yu Hua coming home again, and Tang Yuanyuan also ran away quickly. Come out and stick to Yu Hua.
"Xu Rui, how is the situation at home?" Yu Hua hugged Tang Yuanyuan and walked to the main room.
"Sir, everything is as usual at home. Xu Rui lives in seclusion according to your arrangement and does not interfere with outside affairs. During this period, there have been many shooting cases. I heard that they were committed by Japanese spies." Xu Rui said respectfully.
Yu Hua nodded thoughtfully and asked, "Where is Yuanyuan's mother buried?"
"Xijiao Yiyuan, No. 682." Xu Rui truthfully gave the location of Yuanyuan's mother's grave. "Remember it well. When Yuanyuan grows up, you can bury her again. Come on." Yu Hua came to the front of the main room. After making arrangements, he put down Tang Yuanyuan in his arms and motioned to Xu Erya who was standing aside to watch.
After saying that, he turned around and walked into the main room.
The black and white portrait of Yu Qinghe was placed on the table in the hall. Three incense sticks were burning slowly. Yu Hua stepped forward and knelt down, bowed and kowtowed three times.
After the memorial ceremony, Yu Hua took out three more incense sticks, lit them, and inserted them into the incense burner. The surface of the table was clean, and there were no debris around the main room. Xu Rui and Xu Erya were very attentive to cleaning the main room.
"Xu Rui, Erya, how have you been studying during this time?" Yu Hua finished offering the incense and walked out of the main room. He held Tang Yuanyuan, who was as cute as a porcelain doll, with his right hand and asked Xu Rui and Xu Erya. .
Upon hearing this, Xu Erya lowered his head immediately, feeling a little embarrassed.
"Sir, Xu Rui is good at learning and can read and write. Erya has never been to a private school and lacks a foundation. She is still literate." Xu Rui answered truthfully.
"It's good to be able to read. As long as you have the will, you don't have to worry about failing to learn. There's nothing to be afraid of if your progress is slow. Come on." Yu Hua glanced at Xu Erya who lowered his head and blushed, smiled and comforted.
"Sir, Erya would like to ask you to give me a name." Xu Erya raised his head and glanced at Yu Hua, gritting his teeth and saying as if he had made some important decision.
Yu Hua was stunned for a moment: "Name it? I don't know how."
He doesn't know how to name, an operation that involves the entire life.
In later generations, many people in China did not attach much importance to names and thought they were just code names. However, in this era, names were extremely valued and particular, and they would not dare to give names without any cultural level.
Yu Hua has some level of education, but the problem is... he is a waste of standard naming.
Otherwise, he would not have remained silent when the lighting source was named.
If you don’t understand, don’t get involved.
This is Yu Hua's code of conduct.
"Sir, Erya is not afraid. You can choose whatever you like. Erya doesn't want to be called by this nickname all the time." Xu Erya bit her lip and responded.
As soon as these words came out, the courtyard became quiet.
Xu Rui remained silent and said nothing.
"Brother, what is naming?" Tang Yuanyuan asked curiously, showing her big innocent eyes.
"Just give her a name, such as Yuanyuan." Yu Hua touched Tang Yuanyuan's smooth hair and said with a smile.
Tang Yuanyuan seemed to understand: "Oh? Then call Sister Erya Xu Yuanyuan?"
"Sister Erya's name is not Xu Yuanyuan, your name is Yuanyuan."
Yu Hua laughed and shook his head, looking at Xu Erya in front of him. Sensing Xu Erya's attitude and expression, he sighed, thought about it, and said softly: "You brothers and sisters and I met in the winter, just after the snow fell. How about a name with the character for snow?"
Xu Xue.
I didn't choose a name like Xu Ruoxi, Xu Xuan, etc., just a name that fits the characteristics of a girl.
"Thank you for the name, Mr. Erya. From now on, Erya will be called Xu Xue." Xu Rui thanked him immediately.
"Erya thanks Mr. Erya for the name." Xu Erya, no, now called Xu Xue, with a hint of excitement on his face, saluted and thanked him.
"No, Xu Rui, I have something to tell you. Later you go to the Huangchenggen Bookstore in the north of the city and ask them to deliver the printed collection of questions to the door of Xuanjizhai. The quantity is 500 copies. I have already paid the deposit. The balance is 105 yuan.”
Yu Hua shook his head gently, motioned for the two of them to get up, looked at Xu Rui, and explained carefully: "After delivery, you can move all the question books back home, and deliver 50 question books to No. 4 Middle School at 7:20 every morning. Understand?"
"Xu Rui understands."
Xu Rui, who was smart and clever, immediately wrote down what Yu Hua told him.
"This matter is very important. You must remember that this is 105 yuan. Here it is." Yu Hua ordered, then took out 100 yuan of paper and pen from his body and handed it to Xu Rui.
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