"The limit of the integral sum of function f(x) on the interval [a, b]." Fang Yu stood up and replied.
"The answer is correct. To fully understand the definite integral of the derivative, we must first understand what a limit is and what the limit is. Does anyone know?" Yu Hua motioned Fang Yu to sit down, picked up the chalk with his right hand, and then wrote the definite integral on the blackboard. definition, and then continued to ask.
This question immediately confused most of the students present. After two seconds, Fang Yu stood up, frowning slightly, and said in a somewhat uncertain tone: "The definition of limit is: "When a variable takes infinite values one after another, tends to a fixed value, and ultimately makes the difference between the value of the variable and the fixed value as small as possible. This fixed value is called the limit value of all other values. In particular, when the value of a variable decreases infinitely, it Converging to the limit 0, it is said that this variable becomes infinitesimal. "
"This is Cauchy's definition of limit. Although it is not perfect, it is very helpful for us to understand definite integrals. This is the specific definition and expression of limit. I use mathematical language to express limit..." Yu Hua did not expect Fang Yu could still keep up with her own rhythm, her eyes lit up involuntarily, she nodded affirmatively, turned around, and kept dancing with her right hand holding the chalk, quickly and accurately, and beautiful mathematical characters appeared one by one.
At this moment, the whole class was silent.
Looking at the beautiful but abstract mathematical characters on the blackboard, everyone felt extremely cruel, because everyone watched Yu Hua turn each familiar character into something they could not understand.
When these things are taken apart, everyone knows what the symbols are, but together, what is this thing?
Zhao Anyuan, Fang Yu, Li Jian and others sitting in the first row could barely understand, but it was already quite difficult.
Yu Hua tried his best to explain derivatives, definite integrals and limits in the field of elementary mathematics. However, the reality was counterproductive. As he continued to talk, Yu Hua, who already had preliminary thinking about numbers, unknowingly transitioned to the higher level of mathematics to explain, and then continued to explain. Evolved into numerical ideas for proof.
In the following class, many outstanding students in the Science Class 1 were completely unable to keep up with Yu Hua's thinking rhythm.
It didn't take long for Li Jian to be defeated, followed by Zhao Anyuan and Fang Yu. They all fell into a strange state of self-doubt and looked at each other in silence.
The three of them felt that there was something wrong with their brains. Compared with Yu Hua, they were terribly stupid.
"Click, click, click!" The sound of chalk hitting and rubbing against the blackboard kept coming. The entire blackboard was already covered with a series of proof processes and mathematical formulas.
Looking at Yu Hua on the podium who was concentrating on thinking about mathematical problems, Mr. Luo Wenguang, who was listening quietly to the class, and feeling the confusion of Zhou Yuan and other students around him, he couldn't help laughing and shaking his head, feeling in his heart: "It's true that a young man is better than a young man. The rest of his life has been spent It’s no longer suitable to be in this classroom…”
Yu Hua is no longer suitable to stay in the No. 4 Middle School. His level is far beyond that of his peers. The educational level of a high school is a complete constraint for Yu Hua. Even though he is a math teacher, his academic level is not as good as Yu Hua's.
Luo Wenguang will teach high school arithmetic, but will not study college mathematics and fractions.
"These are the eight common Taylor formulas. Note that the Taylor formula is an equal sign rather than an equivalent. By converting the function into a power function, and then using the principle of higher-order infinitesimals being absorbed by lower-order ones, most limit problems can be solved , and the proof process for this question is like this..."
As the class came to an end, the sound of chalk rubbing against the surface of the blackboard finally ended, leaving eight of the most classic Taylor formulas in calculus on the blackboard.
Yu Hua, who was talking eloquently, turned around and saw a group of students with confused faces. He immediately realized that he was talking too much. The mathematics level of the students was still at the elementary mathematics stage. For them, the Taylor formula of advanced mathematics was involved. Too profound.
"I'm sorry, I didn't teach this class well." Looking at his ignorant but dull classmates, Yu Hua sighed in his heart, put down the chalk helplessly, and apologized softly.
Yu Hua discovered that one of his shortcomings was that he could not accurately suppress his mathematics level and teach relevant knowledge suitable for the stage of his classmates. In a sense, he was not a good mathematics teacher.
Even, very bad.
There is no way around it. It is still too difficult for Yu Hua at this stage to deliberately suppress his active thinking about fractions and real variable function theory to the level of elementary mathematics.
The classroom was quiet and the atmosphere was slightly awkward.
The reason for the embarrassment is that they can't understand the content of Yu Hua's lecture.
What is Taylor's formula?
What are higher-order infinitesimals?
Why do we need to prove the definite integral?
Can this thing be proven?
Since being baptized physically and mentally by Yu Hua's mathematical thinking, everyone has a lot of doubts in their hearts, but they dare not ask questions because they don't even understand the questions themselves, so how can they ask for the answers.
Darling, is this the IQ gap between Yu Hua and us?
"Yu Sheng, what you said is very good, but everyone's level can't keep up with you."
At this time, Mr. Luo Wenguang stood up, encouraged him, and explained that as a math teacher, he gave Yu Hua a privilege: "In my math class from now on, you can study by yourself or take leave, but due to the need to pay attention to classroom discipline, you cannot Disturbing other students."
The voice was calm and natural, without any hint of anger.
Yu Hua's mathematics level has far exceeded that of his peers, so he is not suitable for universal education and should be given special rights to independent learning.
In addition, there is another reason - he can no longer teach Yu Hua.
"Mr. Student Xie."
Upon hearing this, Yu Hua was silent for two seconds. Knowing the meaning of Luo Wenguang's words, he bowed and saluted.
Luo Wenguang smiled: "Go back to your seat. After class, come to the office."
Yu Hua, who had obtained special rights in front of everyone, walked off the podium and returned to his seat amidst the envious eyes of everyone. Mr. Luo Wenguang walked up to the podium, left a sentence of self-study for the class, and turned around to leave.
"Lao Yu, you are this one, this one for life!" After Luo Wenguang's figure disappeared, Zhou Yuan immediately gave him a thumbs up, his words were full of shock and admiration. He was really watching Yu Hua crush the whole class with his wisdom, like It was like a train wheel, rubbing back and forth. The whole class, including Zhao Anyuan, did not dare to make a sound.
What is a god of learning?
This is the true god of learning.
The whole scene was just so over the top.
One class to convince everyone.
Yu Hua laughed and shook his head, without saying a word. He raised the notebook in his hand, indicating to Zhou Yuan to read, and opened the textbook on mathematics again. With Luo Wenguang's words, he could study mathematics without any scruples, and the time he could use every day was greatly increased.
There are 2 arithmetic classes every day, which means that the independent study time increases by 90 minutes, and finally no longer has to suffer the torture of elementary arithmetic classes.
this is a good news.
However, I just don’t know whether the result of waiting to go to the teacher’s office will be good or bad.
After a while, when get out of class was over, Yu Hua closed his book and left the classroom, heading to the classroom office.
After Yu Hua left, the quiet Neo-Confucianism Class 1 classroom instantly fell into commotion, with everyone discussing the first period.
…
Classroom Office.
"Boom!"
Yu Hua stood at the door, straightened his slightly wrinkled collar, and knocked on the door.
"Please come in."
Luo Wenguang's voice came from inside.
Yu Hua pushed the door open and walked in. When he saw Luo Wenguang sitting in his seat, he gently closed the door and went forward to greet him, bowing and saluting: "Sir."
Words contain respect.
"Yu Sheng, do you know why sir called you here this time?" Luo Wenguang smiled calmly and motioned for Yu Hua to sit down.
Yu Hua sat down, maintaining the upright posture a student should have, and shook his head: "Students don't know."
"Your academic level in mathematics, Chinese, English and other minor subjects has far exceeded that of a high school student. Now the education in Peking No. 4 Middle School is nothing more than a constraint for you. Sir, I am here to ask you something. "Have you ever considered graduating early?" Luo Wenguang's back straightened slightly and his face was serious. After a brief explanation, he asked.
Graduating early?
"Is there any talk of early graduation from high school?" After hearing this, Yu Hua was filled with surprise.
