my scientific age

Chapter 132 Graduation Early?

"The limit of the integral sum of the function f(x) over 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 the limit is and what the limit is. Does anyone know?" Yu Hua motioned Fang Yu to sit down, picked up the chalk in his right hand, and then wrote the definite integral on the blackboard definition, and then continued to ask.

This question immediately made most of the students present stunned. After two seconds, Fang Yu stood up, her brows were slightly wrinkled, and her tone was somewhat uncertain: "The definition of limit is: "When a variable takes an infinite value one by one, Tends to a fixed value, and finally 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 is infinitely reduced to make it Convergence to limit 0, the variable is said to be infinitesimal. "

"This is Cauchy's definition of the limit. Although it is not perfect, it has been very helpful for us to understand the definite integral. This is the specific definition and expression of the limit. I use the mathematical language to express the limit..." Yu Hua did not expect Fang Yu was still able to keep up with his own rhythm, his eyes lit up involuntarily, he nodded affirmatively, turned around, and his right hand holding the chalk kept dancing, 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 the characters they knew into things they couldn't 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 were barely able to understand, but they were already struggling.

Yu Hua tried his best to explain derivatives, definite integrals and limits in the field of elementary mathematics. However, the reality backfired. As he talked, Yu Hua, who already had a preliminary mathematical thinking, unconsciously transitioned to the advanced mathematics level to explain, and then Evolve into fractional thinking for proof.

In the next class, many outstanding students in the first class of Science have been 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 silently.

The three felt that there was something wrong with their brains. Compared with Yu Hua, they were terribly stupid.

"Da da da!" The sound of the chalk rubbing against the blackboard continued to come out, and 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 math problems, and Mr. Ren Luo Wenguang, who was quietly listening to the class, he could not help but shake his head with a smile when he felt Zhou Yuan and the other students bewildered around him, and sighed in his heart: "It's really better than the blue, the rest of my life has been Not suitable for this classroom..."

Yu Hua is no longer suitable for studying in No. [-] Middle School. His level has exceeded his peers by too much. The education level of high school is completely restrictive to Yu Hua. Even if he is a mathematician, his academic level is not as good as Yu Hua.

Luo Wenguang will teach high school arithmetic, but will not study high school mathematics and numeracy.

"These are the eight common Taylor formulas. Note that Taylor's formula is an equal sign rather than an equivalent. The function is converted into a power function, and then the principle of high-order infinitesimal being absorbed by low-order can be used to deal with most limit problems. , and the proof process of this question is like this..."

As the class drew to a close, the sound of chalk rubbing against the surface of the blackboard finally ended, leaving eight Taylor formulas, the most classic calculus, on the blackboard.

Yu Hua, who was talking eloquently, turned around and saw a group of students with bewildered faces. He immediately understood that he was talking. The mathematics level of the students was still at the stage of elementary mathematics. For them, Taylor's formula involved in advanced mathematics. too esoteric.

"Sorry, I didn't teach this class well." Looking at the ignorant but sluggish classmates, Yu Hua sighed in his heart, put down the chalk helplessly, and apologized softly.

Yu Hua found that one of his shortcomings was that he could not accurately suppress his mathematics level and teach relevant knowledge suitable for his classmates. In a sense, he was not a good mathematics teacher.

Even, very bad.

There is no way, deliberately suppressing the active fractional thinking and real variable function theory to the initial level is still too difficult for Yu Hua at this stage.

The classroom was quiet and the atmosphere was slightly awkward.

The reason for the embarrassment was that they couldn't understand the content of Yu Hua's lecture.

What is Taylor's formula?

What are higher-order infinitesimals?
Why do definite integrals need to be proved?

Can this thing prove it?

Since receiving the baptism of mathematical thinking from Yu Hua, everyone has a lot of doubts in their hearts, but they dare not ask questions, because they don't even understand the question itself, so how can they ask the answer.

Darling, is this the IQ gap between Yu Hua and us?
"Yu Sheng, you speak very well, but everyone can't keep up with you."

At this time, Mr. Ren, Luo Wenguang stood up, encouraged him, explained, and then, as Mr. Math, gave Yu Hua a privilege: "In my math class, you can study by yourself or ask for leave, but because you pay attention to classroom discipline, you can't Disturb other students."

The voice is calm and natural, without any anger.

Yu Hua, whose mathematics level has far surpassed his peers, is not suitable for universal education, and should be given special rights to autonomous learning.

In addition, there is another reason - he can no longer teach Yu Hua.

"Mr. Xie, student."

When Yu Hua heard this, he was silent for two seconds, knowing the meaning of Luo Wenguang's words, and saluting.

Luo Wenguang smiled: "Go back to your seat. After class, come to the office."

Yu Hua, who was granted special rights in front of everyone's eyes, walked off the podium and returned to his seat under the envious gaze of everyone. Mr. Luo Wenguang stepped onto the podium, left a sentence of self-study for the whole class, and then turned and left.

"Lao Yu, you are this, this is the one for a lifetime!" After Luo Wenguang's figure disappeared, Zhou Yuan immediately gave a thumbs up, his words were full of shock and admiration, he was watching Yu Hua crush the whole class with his wisdom, like Like a train wheel, rubbing back and forth, the whole class, including Zhao Anyuan, did not dare to make a sound.

What is a scholar?

This is the real god of learning.

The whole scene is just too exaggerated.

One class, overwhelm everyone.

Yu Hua smiled and shook his head without saying a word. He raised the notebook in his hand and signaled Zhou Yuan to read a book. The whole person re-read the teaching material for scoring. With Luo Wenguang's words, he could study scoring without any scruples, and the time he used every day was greatly increased.

There are 2 math lessons every day, which means that the self-study time increases by 90 minutes, and finally you no longer have to suffer from the torture of the first math course.

this is a good news.

However, I just don't know if it's good or bad to wait in the teacher's office.

After a while, when it was time for get out of class, Yu Hua closed the book and left the classroom, heading to the classroom office.

After Yu Hua left, the quiet and quiet classroom of the first class of Science fell into a commotion, and everyone was discussing the matter of the first class.

……

classroom office.

"Dong dong!"

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 open the door and entered, saw Luo Wenguang sitting on the seat, gently closed the door, greeted him, and saluted, "Sir."

Words imply respect.

"Yu Sheng, do you know why Mr. called you this time?" Luo Wenguang smiled and said calmly, motioning Yu Hua to sit down.

Yu Hua took his seat, kept his proper posture as a student, and shook his head: "Students don't know."

"Your academic level in arithmetic, Chinese, English, and other secondary sciences is far higher than that of a senior middle school student. Now, the education of Peking No. [-] Middle School is like a kind of restraint for you. Sir, I am here to ask you a question. Have you considered graduating early?" Luo Wenguang straightened his back slightly, his face was serious, and after a brief explanation, he asked.

Graduating early?

"What about graduating early in high school?" Yu Hua was full of surprises after hearing this.

(End of this chapter)