my scientific age

Chapter 36 Functions
Speech is solemn and solemn.

Hua Luogeng is a full professor of National Tsinghua University. He has just returned from studying in the UK and has a very deep knowledge in the field of mathematics. Luo Wenguang does not want this group of students to offend Hua Luogeng.

It has to be said that the content announced by Mr. Ren Ren is very important. Like dropping a huge stone on a calm lake, it immediately set off a huge splash of water and bursts of waves. There were 22 students present in the classroom, including Yu Hua. Inwardly, everyone was moved by it, and their hearts were full of surprise and shock.

Inviting Hua Luogeng, a professor of mathematics at National Tsing Hua University, to teach in person, what kind of treatment is this?

"It's awesome..." Yu Hua swallowed his saliva, and his heart was shocked. He was in awe of the school's approach. To be honest, he had never seen such a situation. Even in later high schools, he did not invite Tsinghua University professors to give lectures. Case.

It is not an exaggeration to call this unprecedented.

Most importantly, Hua Luogeng was invited by Peking No. [-] Middle School!

The man who will stand at the pinnacle of Chinese mathematics in the future, Hua Luogeng, known as the father of modern Chinese mathematics!

Looking at the reactions of the students, Mr. Class Ren Luo Wenguang nodded with satisfaction, turned his head, smiled slightly at Hua Luogeng, and immediately stepped aside, motioned to step forward, and then retreated to the door of the classroom.

"Hello students."

Hua Luogeng stepped forward generously, stood in the center of the podium, looked around, found a familiar face in the crowd, smiled and greeted.

"Students meet Professor Hua Luogeng."

In a flash, all the students reacted as if they had just woken up from a dream, raised their hands, leaned forward, and bowed to Hua Luogeng on the podium.

"Sit down, classmates, today I was invited to come to Beiping No. [-] Middle School to give a lecture to everyone. To be honest, this is my Hua Luogeng's honor. After all, my education is only junior high school, and all of you here are high school students. With a smile on his face, Hua Luogeng pressed his hands down to signal everyone to sit down. After all the students had sat down, he began to speak. There were emotions and expectations in his words, and finally he couldn't help but tease.

Junior high school education.

Yes, Hua Luogeng, a professor at the National Tsinghua Mathematics Department, has only a junior high school education, which is one of Hua Luogeng's distinctive features.

One of Hua Luogeng's life can be described as a legend. When he was young, his family was poor and his business was bleak, which made him unable to maintain expensive reading expenses. Hua Luogeng couldn't continue his studies. He had to drop out of junior high school and returned home to help his parents with the business.

However, after graduation, Hua Luogeng did not give up his studies. He helped while studying. With the help of his teacher, he completed all the mathematics courses in high school and university in only five years. The talent and talent are extremely terrifying, and the level of mathematics is not at all. Less than the mathematics professors of various universities at that time.

With the theory of "The Reason Why Su Jiaju's Algebraic Quintic Equation Solution Can't Be Established", Hua Luogeng became famous at a young age and caused a sensation in the entire Chinese mathematics community. He finally entered Tsinghua University as a librarian and did not explain himself at first. 's open life.

From librarian to National Tsinghua mathematics professor, Hua Luogeng took only seven years.

In the classroom, all the students in the first class of Science became happy when they heard Hua Luogeng's humorous self-evaluation, and many people even laughed out loud.

Really big guy.

A self-introduction can mobilize the audience.

Yu Hua looked at Hua Luogeng on the podium, and sighed in his heart, but there was a trace of imperceptible envy in his eyes. He also hoped that one day he could stand on the podium of No. [-] Middle School and talk so eloquently.

"In terms of academic qualifications, you are high. In terms of level, I, Hua Luogeng, are higher. Today, the content of arithmetic I will teach you is - functions." Hua Luogeng pushed his glasses, picked up the white chalk on the lecture table, turned around, Under everyone's attention, two block and traditional Chinese characters were written.

function?

Looking at the two big characters on the blackboard, and then at Hua Luogeng who was smiling, all the students were a little puzzled.

Yu Hua's face was natural, and his bright eyes stared at Hua Luogeng. He had no doubts, no doubts, and waited with peace of mind.

The number one in the class, Zhao Anyuan, straightened his body and looked focused. He was obviously energized. He was holding a pen in his right hand, and a notebook appeared on the desktop at some point.

"Functions, the content of Chapter 1 of High School Mathematics. Today we don't talk about probability and statistics, and we don't talk about derivatives that are a headache for you. We only talk about the importance and significance of functions."

Hua Luogeng spoke calmly, neither too fast nor too slow. He spoke in the way he was accustomed to: "First of all, what is the importance of functions? Basics. Looking at all the high school arithmetic books in the past three years, any knowledge in mathematics is not necessary. Functions are used as a guide. Regarding my statement, you can review, when you do topics such as trigonometry, analytic geometry, probability statistics, etc., whether the topics will involve some knowledge points of functions."

The voice was in his ears, Zhao Anyuan nodded thoughtfully, and the rest of the students fell into thinking, briefly reviewed them, and all admitted.

Indeed, as Professor Hua Luogeng said, functions run through almost the entire high school arithmetic line.

When Yu Hua heard this, he sighed in his heart that Mr. Hua Luogeng is really good. In later high school mathematics, functions are the first mathematical knowledge points that students come into contact with. They seem simple. In fact, few students really understand that functions are actually the whole high school mathematics. The hardest math section.

Among the mathematics questions of the college entrance examination in later generations, the combination of functions and derivatives can make countless students numb their scalps, and the combination of number sequences and inequalities is a direct explosion.

What is a sequence of numbers essentially?
or function.

"Functions can be said to be the only knowledge point that runs through the entire high school arithmetic. The derivative that troubles you is called derivative in mathematical language. It is the local property of function. In layman's terms, derivative is just a tool of function. There are many changes, and it requires rigorous logical thinking to understand. It can be extended to the field of calculus at the university level, which is of great significance. Who knows the definition of classical functions?" After Hua Luogeng finished speaking, he turned his eyes to the bottom of the podium.

In an instant, all the students raised their hands immediately.

"Just the last student." Hua Luogeng pointed at Tan Qing who was in the last row casually.

"Mr. Hui, the classical function is defined as: for every definite x value in a certain interval, y has a definite value, then y is called the function of x." Tan Qing, who was looking forward to it, saw Hua Luogeng actually named him Surprised in his heart, he quickly stood up, lowered his head slightly, and replied.

Hua Luogeng smiled slightly: "That's a good answer, what about the modern definition of a function?"

"Modern definition of function: Given a number set A, assuming that the element in it is x, apply the corresponding rule f to the element x in A, denoted as f(x), to obtain another number set B, assuming that the elements in B are y, then the equivalent relationship between y and x can be represented by y=f(x), and the function concept contains three elements: domain A, value domain B, and corresponding law f.” Tan Qing continued to answer.

After listening to it, Hua Luogeng motioned for Tan Qing to sit down, picked up the chalk in his right hand, turned to face the blackboard under the watchful eyes of the students, and wrote a function problem.

Set A={(x,y)|Y=a}, set B={(x,y)|y=bx+1, b>0, b≠1}, suppose set A∩B has only one subset, Then what is the range of values ​​for the real number a.

(End of this chapter)