Chapter 173

“...... Finally, I'm going to talk about the rest of Taylor's expansion. ”

"The remainder of Taylor's formula, Rn(x), can be written in several different forms. ”

"Nopea remainder: Rn(x)=o[(x-x0)^n]!"

"Schlemirch-Rosch remainder: Rn(x)=f^(n+1)[x0+Θ(x-x0)]......"

"Lagrange Remains!"

"Cauchy Remains!"

"And finally, the remainder of the points!"

"You must keep in mind the definitions and contents of these remaining items, as well as the methods of operation!

The remaining five items of Taylor's formula are even more terrifying than Taylor's formula itself.

Most schools, even if they get this part of the content, will only look at the simplest Lagrange remainder.

But if you look through the final exam papers of Yan University's high mathematics in previous years, you will find that the group of teachers in the high mathematics proposition group of Yan University are completely frenzied.

The five remaining forms of Taylor's formula, the teachers in the proposition group will not pick the simplest Lagrange remainder terms.

What is the rest of Nopea, the rest of Schlemmerch-Roche, so it's enjoyable!

It is guaranteed that the tortured students want to die and can't stop.

At the same time, it is a great challenge for the students' comprehension ability.

When the bell rang for the end of class, Gu Lu just finished talking about the five remaining forms of Taylor's formula.

"In the next class, I will do the consolidation practice of Taylor's formula, and when you go back, you will digest this knowledge. If you don't understand, you can ask your classmates, or you can ask me in the WeChat group, or go to the office. ”

"Alright, this class is here, class is over!"

After speaking, Gu Lu carried his bag and strode out of the classroom.

In the classroom, a female classmate rested her chin on the table without love.

"Yifei, what's wrong with you?" asked a girl next to her.

"I didn't understand the five forms of Taylor's formula that Mr. Gu talked about just now. However, I feel like I'm in love with the high math teacher!"

"What do you mean by that?"

"Because in front of the person you love, the IQ is basically zero. ”

“......”

It's not funny at all.

............

Back to the office.

Take off your trench coat and hang it on a hanger.

The warm feeling of being wrapped in the office heating made Gu Lu extremely comfortable.

Looking out the window, there was a sign of silence on campus.

Sure enough, in the winter, except for necessary activities such as classes, even the students rarely come out.

Rubbing his hands, Gu Lu made a cup of coffee and drank it in small sips while working.

The work of preparing for the class has already been completed.

Gu Lu is now working on the second problem of the minimalist program.

Because Senior Brother Gao considered Gu Lu and still had daily teaching tasks.

Therefore, in the final paper writing session, Gu Lu is mainly responsible for the first part, that is, the proof that the flip operation of a three-dimensional algebra cluster terminates after a finite number of times.

The proof process of the high-dimensional algebraic cluster that occupies more than half of the space and ends after a finite number of flip operations is sorted out by Senior Brother Gao.

Gu Lu was tidying up here, and Teacher Shi in the same office hurriedly pushed the door and walked in.

After searching the office, his eyes finally fell on Gu Lu.

Then, he walked straight towards Gu Lu.

"Teacher Gu, are you free for the third or fourth session tomorrow morning?" asked Teacher Shi directly to the point.

Gu Lu looked up suspiciously, then thought for a few seconds, and nodded, "I didn't have classes during that time period." Teacher Shi, you are ......"

Teacher Shi shook his head, looking distressed, "My son's school is going to have a parent-teacher conference, and it will be tomorrow morning." My wife's unit is strict, and I really can't spare time, so I can't only go!"

"But tomorrow morning, three or four periods, I happen to have one more class, Teacher Gu, can you go to a class for me?" Teacher Shi asked with a smile.

"Me?" Gu Lu pointed to himself, smiling a little disbelievingly, "Teacher Shi, do you want me to teach for you?"

Mr. Shi taught "Real Variable Functions and Functional Analysis" in the third year, while Gu Lu taught "Mathematical Analysis" in the first year.

It's two courses with different levels of difficulty.

Gu Lu couldn't figure out the reason why the teacher let a new teacher who had just arrived go to substitute for the class.

Is it love?

Is it trust?

No, it's just because tomorrow there will be a random class sampling by school leaders!

Teacher Shi was worried that his class would be drawn, so he came to Gu Lu for help.

"Teacher Gu, the content you are responsible for is very simple, put the thirteenth to twentieth pages of the PPT, and tell them according to the content on the PPT, and then I assigned ten practice questions, the questions and answers are in this USB flash drive, you supervise the students to do these ten questions, it doesn't matter if you talk about it or not, just get the answers right. Teacher Shi handed a USB flash drive to Gu Lu.

"It's that simple?" Gu Lu wondered.

"Yes, it's as simple as that. Teacher Shi patted Gu Lu on the shoulder, "Teacher Gu, when the time comes, you can just play as you please, and you don't have to worry about making mistakes." ”

I'll do it again later, anyway.

Teacher Shi silently added in his heart.

Anyway, it was just to survive the inspection of the school leaders, and Teacher Shi didn't expect Gu Lu to be able to give a wonderful lecture.

Real function and functional analysis are extremely difficult to teach.

Not only did the students have a hard time listening, but even the teachers struggled to make sure the students could understand it thoroughly.

In order to prepare for this course, Mr. Shi took a lot of effort.

Teacher Shi did not expect Gu Lu to be able to thoroughly understand this course in less than a day, and in tomorrow's class, he only needs to draw a scoop according to the PPT and practice questions provided by himself, and everything will be fine after two classes.

Gu Lu was here, and after a few seconds of silence, he nodded, "Okay, Teacher Shi." I'll follow that tomorrow. ”

Teacher Shi's face was happy, "Teacher Gu, you have done me a great favor." Don't worry, I remember your favor. If you encounter anything in the future, you will definitely help if you can. ”

After speaking, Teacher Shi left humming a little song.

Gu Lu shook his head with a wry smile, plugged the USB flash drive into the computer, opened the PPT, and looked at it page by page.

The real function and functional analysis are divided into two volumes.

In the first volume, we mainly talk about real variable functions.

In the second volume, we will focus on functional analysis.

I am now in the first half of my junior year, and I am mainly learning the content of real variable functions.

............

Real variable function.

It's a simple four words, but for the students of the mathematics department, it is a terrifying existence.

Although it is only one word different from the complex variable function, the difficulty of the two courses is not at the same level at all.

If you hold a poll, let the students of the Department of Mathematics choose the most difficult major course at the undergraduate level.

The real variable function, it is absolutely not surprising that it will win the top spot with a high number of votes.

Without him, it's because it's so hard.

The real variable function is studied ten times.

However, even after ten times, there are still many people who can't learn.