"Huh? Su Mu, are you actually looking at advanced mathematics? ”

In a chance math class, when Ou Dao was about to leave the classroom, he was surprised to find the advanced math book on Su Mu's desk, as well as a dense stack of scratch paper.

In fact, Su Mu has been brushing for two or three days, but Ou Dao has not noticed.

According to Su Mu's plan, he wanted to brush the math to level six at one time to see if there were any new functions in the system.

Of course.

He now has a strong interest in mathematics and is one of the motivations for brushing up on problems.

"Where have you learned?" Ou Dao stopped walking out of the classroom and suddenly became interested.

"It's just the beginning, I'm learning the law of Lobida and Taylor." Su Mu said truthfully. "But this knowledge is too scattered, and I'm going to sort it out systematically."

Ou Dao nodded, picked up Su Mu's scratch paper and looked at it, his eyes lit up.

Through these arithmetic symbols, he knew that Su Mu had entered the door.

"Teacher, but I still have a few questions."

Su Mu has indeed encountered some bottlenecks in the past few days, and now he happened to be seen by Ou Dao, so he asked.

"It's just that the connection between differentiation and derivation is so complicated that I don't know where to start for a while."

Ou Dao pondered for a moment.

"Have you learned the Cauchy median value theorem and the Lagrangian median value theorem?"

Su Mu nodded.

"As I have seen before, the Lagrangian median theorem reflects the overall average rate of change of a derivative function over a closed interval as a function in relation to the local rate of change at a point in the interval."

"Cauchy's median theorem is a formulation of the Lagrangian median theorem under parametric equations, stating that a given plane arc between two endpoints has at least one point such that the tangent of the curve at that point is parallel to the string where the two endpoints are located." Su Mu replied.

"Not bad."

Ou Dao's eyes showed a little appreciation.

He explained: "But what you are talking about is the geometric meaning of Cauchy's median value theorem. ”

"But from the perspective of application, it is to prove the nth-order Taylor formula with a Lagrangian remainder, which can be proved by repeatedly using Cauchy's median value theorem many times."

"Lobida's law is a simplification that satisfies fixed conditions, or creates conditions that do not meet them."

"Among the three differential median theorems, there is also a Rolle's theorem, you can also take a look for yourself, many things are common in it."

"What about the relationship between derivatives and differentiation?" Su Mu nodded thoughtfully.

"The derivative originates from the rate of change of the value of the function with the increment of the independent variable, that is, the limit of △y△x, and the differentiation originates from the microanalysis, such as △y can be decomposed into the sum of the two parts of A△x and o(△x), and its linear main part is called differentiation, you should be able to understand this, right?"

"Hmm." Su Mu nodded. "It's the rate of change and the limit"

"Differentiation is a method of taking the tiny variables or microelements of an object to deal with mathematical problems, and the derivative is the limit of the differentiator, basically, the derivative is the quotient of the differential, and for the unary function, the derivative must be differentiated, and the differentiation must be derivable."

"Both differentiation and derivatives are used to study the properties of functions, to solve the maximum-value problem, or to prove inequalities, to study the real roots of equations, and so on."

"Do you understand what I'm saying?"

"I...."Su Mu frowned, he seemed to understand, but he didn't seem to understand.

Sighing: "I'll see for myself." ”

Ou Dao smiled: "It's okay, you look slowly, I see that the calculations you calculated on the scratch paper should not be a big problem for the functions and calculus you learned in high school." ”

Seeing Su Mu working so hard, he couldn't help but have a look of relief on his face, but he didn't expect that after a winter vacation, Su Mu's mathematical level had improved to this point.

Suddenly thinking of something, Ou Dao said. 600

"By the way, do you want to go to the National High School Math League?"

"Math competition?" Su Mu asked.

"It's pretty much the same, but this is not organized by various provinces and cities, but a national-level competition."

"After the follow-up promotion, it is the Chinese Mathematical Olympiad and the International Mathematical Olympiad, although it has not been added to the college entrance examination in recent years, but it has a great advantage in the independent enrollment of major universities."

Su Mu thought for a moment and nodded: "Do you need to prepare anything for registration?" ”

He doesn't care about the extra points in the college entrance examination, with his current grades, he can basically go to any school.

However, he is still very interested in math competitions.

If you win a prize in such a big competition, you will definitely increase your math points.

You might even get skill points.

"The provincial preliminaries should be held at the end of April, and there is still more than a month, so it will definitely be no problem to report on your terms."

"You can buy a series of books guided by the High School Math Olympiad first, the one edited by Ge Jun is very good."

"If you pass, you can participate in the National High School Math League, which is held in mid-October every year."

Ou Dao explained.

Su Mu nodded: "Okay, then I'll go buy a copy this weekend." ”

In my heart, I always felt that the name Ge Jun was a little familiar.

Ou Dao nodded with satisfaction, and turned his head to look at Yan Xiaoke, who continued to maintain a stunned state on the side.

"Xiaoke, are you interested in participating? Your math foundation is pretty good, too. ”

"The red-headed document hasn't come down yet, but it should be soon."

"I....?" Yan Xiaoke's heart was now in a crazy mess, and he bit his lip: "Can I?" But I don't seem to understand what you just said, I only know Cauchy's inequality, I don't know Cauchy's median value theorem. ”

"No, no, we just talked about advanced mathematics, which has little to do with the league." Ou Dao waved his hand and said with a smile.

"With your grades, I think you have some chance of passing the provincial exam, I remember that you scored more than 140 points in math last time, right?"

Yan Xiaoke nodded.

"But you can also learn more from Su Mu, and you can also follow him to read this book of advanced mathematics, there is no harm."

A strange feeling suddenly rose in Yan Xiaoke's heart.

From childhood to adulthood, basically all the teachers let Su Mu learn more from him.

This is the first time that a teacher asked her to learn more from Su Mu.

Ou Dao wanted to say something more, but the class bell rang suddenly, and physics teacher Wang Sizhong walked over with a stack of test papers.

Ou Dao greeted Wang Sizhong with a smile, and after telling Su Mu to study hard, he finally left the classroom.

Su Mu: "....."

Yan Xiaoke: "......"

Su Mu and Yan Xiaoke looked at each other.

Half a day.

Su Mu asked weakly.

"Do you need me to come home at night and help you with math?"

.....