Lu Yonghua thinks about it, from his point of view, it is rare that these people who do not study are willing to learn a little, although they can't learn much, but they do a little bit.

For the sake of the students, it makes sense to let Wen Xiaoguang come over and talk about it.

The interaction between the students has improved, which is a good thing from a certain point of view.

This is a good teacher.

"Okay, come up, and talk to us all about the last question of finding area. Lu Yonghua suddenly said: "It seems that you don't like to listen to me, you love to listen to him, it's okay, as long as you can learn more, it's always a good thing." ”

This old boy is witty and simple, this is a reaction, he can achieve good results without contribution, and he will say that he is an innovative classroom form, killing three birds with one stone.

"Come on, come on, try, if the effect is good, we will let Wen Xiaoguang give us more lectures in the future. ”

Wen Xiaoguang was speechless, this is not nine years of compulsory education, I will teach you every day, I still have to pay money when it is over, right?

Did you know that Dr. Wen's hourly salary is 300 yuan?

Fang Zhisuke had already moved out of the way and watched his table mate walk onto the podium.

"Teacher Lu, let's talk about the last question directly?"

"Of course, interest-based teaching is the best. You can simply talk about calculus, you know how much you say, it doesn't matter, I'll add. Five minutes, more than a waste of time. ”

Supplement?

You're thinking too much.

Lu Yonghua gave him the chalk and went to the back of the classroom by himself, "Chen Tian, you have to listen, I'll ask you questions in two days to see if you are serious." ”

The classmates covered their mouths and laughed.

Wen Xiaoguang, who was on the podium, turned around with a chalk, wrote neatly on the board, and wrote down the three words calculus.

"As for calculus, in fact, Mr. Lu also introduced it to us in the mathematics course of the second year of high school, that is, the concept of derivatives,"

He draws a number line on the blackboard and a curve in the first quadrant.

"Suppose the function y=f(x) is defined in this interval and has two points A and B. The difference between the ordinates of two points is greater than the difference between the upper abscissa Δy /Δx is the derivative of point A, which is very simple. ”

"If we express the increment Δy of the function Δy = f(x + Δx)– f(x) as Δy = AΔx + o(Δx) (where A is a constant independent of Δx), then o(Δx) is infinitesimal higher order than Δx, then the function f(x) is differentiable at the point x, and AΔx is called the differentiation of the function at the point x0 corresponding to the independent variable increment Δx, denoted as dy, i.e., dy = AΔx. ”

This is what we call differentiation, and integration you can understand as the inverse operation of differentiation, that is, to know the derivative of the function, to find the original function, in the application, the role of the definite integral is not only that, it is widely used in summing, in layman's terms, to find the area of the curved triangle, just like the last question of the test paper. ”

Lu Yonghua stood behind and looked at Wen Xiaoguang, who was writing and talking, nodded frequently, yes, yes, differentiation and integration are like this.

It's not hard for him.

But for students at this stage, it is still a bit difficult.

A lot of people are confused, do you learn these things in math after high school?

Is it too late to drop out?

Wen Xiaoguang is not a self-congratulatory player, he probably collected a little bit of the expressions of his classmates, and then said: "Calculus is relatively rare for middle school, and there are many contents, differential calculus includes limit theory, derivatives, and differentiation, and integral science includes definite and indefinite integrals. So get a rough idea of ......"

Chen Tian was not convinced, "You said so much, what the hell is this?"

Wen Xiaoguang sighed, put down the test paper, and told the story.

"There have been three crises in mathematics, the second of which was the questioning of the weak foundations of calculus. He turned around and circled 'Δy/Δx' with chalk, "At that time, people and you all had a question, they all said that Δx is close to infinitesimal, so what is infinitesimite? If it is 0, 0 cannot be the denominator, if it is not 0, then how can it be said that point B is point A, is this incomprehensible?"

Generally speaking, this is the case, and people who are new to it are resistant to the limit theory because it does not conform to our normal logic.

Calculus was founded in the seventeenth century by Newton and Leibniz, both of whom fought for it all their lives, but neither of them came up with a perfect definition of infinitesimal because they questioned the theoretical basis of calculus, the so-called second mathematical crisis, which lasted for 150 years. ”

Speaking of which, the children of Class 8 were interested.

"Then who solved it?"

"Wasn't Newton a physicist? He could do math?"

......

"Newton was good at mathematics and was hailed as one of the four great mathematicians. As for this crisis, it is not solved by one person, but a number of mathematicians have jointly perfected this definition," Wen Xiaoguang patiently replied: "Lagrange was the first to make calculus rigorous, and he tried to base the entire calculus on Taylor's formula; Cauchy based calculus on limit theory; Weierstrass logically constructed the theory of real numbers; Riemann proved that the integrand is not continuous, and its definite integral may also exist, and improved the Cauchy integral to the Riemann integral." ”

The classmates looked confused, he didn't have a single letter in what he said, it was all Chinese characters, but I really didn't understand, the key was that I hadn't heard of any of the names.

Simple students still don't understand that these are names that you will never forget in your life.

Even Lu Yonghua subconsciously touched his head when he heard it, ah, bare.

"Wen Xiaoguang, you go on, what is calculus?" Chen Tian shouted again.

Wen Xiaoguang is strange,

"I'm done," he circled a formula, "that's differential, and as for the integral sign, it's probably like a fallen s." As for the theoretical concepts, it's probably in the story of the second mathematical crisis, and it's all over, haven't you listened?"

Chen Tian: "......"

You drew two strange symbols and told me about it?

Lu Yonghua didn't look at him, and said loudly: "The basic concepts of differentiation and integration don't sound easy to understand for the first time, so you can use the last question to talk about the application." ”

"Well, in fact, although I don't learn calculus in high school, whether it's physics or mathematics, some problems are actually easier to learn using calculus, if you want to get a score on this, you can try to use this kind of thinking and method, it is very effective. ”

"If you really don't want to...... That's okay," Wen Xiaoguang smiled, "Anyway, I can't run away when I get to college." ”

Class 8 students silently recited a sentence in their hearts. Then I'd better not take the university entrance exam!

I talked a little bit about mathematics in five minutes, and then it wasn't so fun to go back to the question itself, but Lu Yonghua found that because it was Wen Xiaoguang's lecture, many girls didn't understand it or not, and the notes remembered that they were serious thieves.

And because he found time to stand in the back, the students were much more honest.

Mom, this works well!

Last time he talked about the test paper, he sat in front of him, and he didn't expect this kind of unexpected gain!

The key is that Wen Xiaoguang really spoke well, in simple terms, simple and easy to understand, and was comfortable with mathematical knowledge points and theoretical applications.

At the end of class, because this test paper was difficult, he didn't finish it, and he also told Wen Xiaoguang: "Make some preparations for the rest of the content, and I'll talk about it next time." ”

"Good. ”

What a good!

Lu Yonghua is crazy,

But the classmates sitting in the back are really crazy,

Dai Weiyi joked, "Wen Xiaoguang! It's because of you that we have a bad time in math class! Everyone listens to my orders and beats him for me!"

Seven or eight people who usually joke with each other all at once,

"Wen Xiaoguang, don't run!"

Don't run?

It's a fool not to run to labor!