Chapter 144

"What, Mr. Gu graduated from Princeton?"

"I got a doctorate in two years, which is too dick!"

"——! is still an assistant at the Institute of Advanced Mathematics, and I have nothing to say except worship. ”

"Bi Qi, is our Teacher Gu really so strong?"

"That's!" said Bizzie, holding his head high, with a sense of pride.

If it weren't for Teacher Gu being so strong, how could he take Teacher Gu as his goal.

"Now you should always believe that Teacher Gu has the ability to teach us the course of mathematical analysis, right?" said Bi Qi with a smile.

"It's really much more reliable than before. Zhang Zhenzhen nodded approvingly, "I didn't have any bottom at all before. ”

"But before Mr. Gu actually gave a lecture, I was still skeptical. Zhang added in a moment.

Bi Qi hugged his arms and smiled faintly, "I think soon, you will change your mind." ”

…………

Gu Lu took out the textbook of "Mathematical Analysis" from his bag.

At present, most of the mathematics textbooks used by colleges and universities are blue books published by Fudan University Press.

But Yan is very different.

Most of the textbooks for the Mathematics Department are basically textbooks published by Yan University Press.

Mathematical Analysis is no exception.

In the Department of Mathematics of Yan University, the textbook of mathematical analysis is a yellow-covered book compiled by Mr. Wu Shengjian.

There are three volumes, one book per semester, and they are completed in three semesters.

Gu Lu is currently responsible for the teaching of the book "Mathematical Analysis (I)".

He glanced at the audience and held up the textbook in his hand.

"Students who have studied this course during the summer vacation raise their hands?" asked Gu Lu slowly.

Whew!

Forty-five students raised their hands in unison.

"Not bad. Gu Lu nodded with satisfaction, and then asked, "Then after the preview, one student raised his hand." ”

There were only about twenty people left who raised their hands.

The students who had finished previewing the books raised their hands. ”

There were only seven or eight people who raised their hands.

"Count one, two, three, and all three books have been previewed?"

This time, only three people raised their hands.

Bi Qi and Ma Zhengxuan, who sat in the first row, and the only female classmate in the class who sat in the back row.

Gu Lu's gaze fell on the girl in the back row.

"Classmate, what's your name?"

"Teacher, my name is Bai Yao. Bai Yao got up, her eyes flashed moving, and a pair of bright eyes stared straight at Gu Lu.

Bai Yao!

Hearing this name, Gu Lu didn't do much, but the other students in the class were not calm at first.

Bi Qi glanced at Zhang Zhenzhen, who was full of surprise, and asked, "What, do you know this person?"

Zhang shook his head, "I don't know, but I've heard of his name for a long time." ”

Zhang said in a deep voice, "This Bai Yao should be the top student in our science college entrance examination in Yanjing City this year." ”

Is it another top student in the college entrance examination?

Bi Qi turned his head to look at Bai Yao in the back row, his eyes were deep.

There are more than 30 science champions in the national college entrance examination.

But their mathematics department includes two of them.

There are more than a dozen people in the top 10 in each province.

In addition to a few escort students.

This year's Department of Mathematics of Yan University is enough to describe it as full of talents.

On the stage, Gu Lu picked up a piece of chalk and said with a smile, "In the first class today, before the lecture, let me test your preview results." ”

"I'll have a few questions on the blackboard in a moment for you to answer. There is no penalty for answering incorrectly, but there is a reward for answering correctly. ”

"Your final grade in the course of Mathematical Analysis is 80% in the final exam and 20% in the usual grade. What is the measure of grades? One is attendance, and the other is classroom performance. ”

"I don't know what other teachers are like, but that's how I made it. The usual score is 100 points, 5 points are added for class performance, 5 points are deducted for being late, and 10 points are deducted for absenteeism. That said, we math students should know it very well. ”

"Next, I'll start with the question. ”

After speaking, Gu Lu turned around and wrote the title on the blackboard.

Since it is a test of the results of the preview, the difficulty of the question will definitely not be too high.

Gu Lu came up with four questions according to the principle of going from difficult to easy.

[1. Discuss the divergence of the sequence: an=n√(1+n√(2+n√(3+......+n√n).]

[2. Let f(x)∈C[a,b],f(a)=f(b), prove: there is a series xn, satisfying xn

[3. Proof ∑: n, k=0(-1)^kC: kn(1/1+k+m)=∑:m, k=0(-1)^kC:km(1/1+k+n).]

[4. Find the function f(x)=2xsinθ/1-2xcosθ+x^2 in the Taylor expansion of x=0, where θ is a constant, and calculate the integral ∫(π,0)ln(1-2xcosθ+x^2)dθ.]

Four questions, gradually increasing in difficulty.

Gu Lu wrote the four questions on the four blackboards, then turned around and looked at the people below, "Who will come to the first question?"

"Teacher, me!"

"Teacher, let me go. ”

"Teacher, flip through my sign!"

Many people below raised their hands.

The first question, the easiest of the four, is naturally contested by many people.

However, there were also a few people who did not raise their hands.

For example, Bi Qi and a few people sitting in the first row, and Bai Yao, who sat in the back.

It's not that they won't.

Rather, they don't bother to do such a simple problem, so they give the opportunity to someone else.

"Come on, then this chubby classmate. Gu Lu flipped through a chubby boy's sign, and after asking the name, he handed him a piece of chalk and stretched out his hand to signal him to answer the question.

By the second question, there were many fewer students raising their hands.

Gu Lu ordered a boy sitting in the second row.

In the third question, there are not many people who raise their hands.

Most of the students are writing and drawing on the paper while frowning and thinking about the solution ideas.

Although Gu Lu said that there is no punishment for answering wrongly.

But if you go up without preparation, and the result is not made, wouldn't it be very embarrassing to be watched by more than 40 students below.

"Zhengxuan, no problem, right?" Gu Lu handed the chalk to Ma Zhengxuan in the first row.

"No problem. ”

Ma Zhengxuan got up, and then walked to the podium without hurrying, basically didn't see that he had time to think, so he wrote the formula with chalk on the blackboard.

【1/1+k+m=∫(1，0)x^(k+m)dx，

∑：n，k=0(-1)^kC:kn(1/1+k+m)=∫(1，0)∑：n，k=0(-1)^kC:knx^(k+m)dx=∫(1，0)x^m(1-x)^ndx.

The same can be obtained ......]

Ma Zhengxuan's writing is very smooth.

"The last question, is anyone willing to try it?" Gu Lu swept over the students in the audience.

Many classmates and Gu Lu looked at the present, and lowered their heads in cringe.

For the fourth question, many students subconsciously have the idea of escaping after reading the question.

That's Taylor's formula!

Mathematical analysis is one of the most difficult to understand in the entire course.

Moreover, Mr. Gu's set of questions seems to be not only a simple deformation of Taylor's formula, but also ...... It's more complicated.

In their opinion, this question is enough to be used as the finale of the final exam.

But now, it's up to a group of freshmen who have just entered the school.

How could anyone be?

But at the moment when the idea of everyone appeared, the two hands were raised at the same time, almost in no particular order.

"Teacher, I'm coming!"