Chapter 144

"What, Teacher Gu graduated from Princeton?"

"Getting a doctorate in two years is so awesome!"

"Hiss—! I'm still an assistant at the Institute of Advanced Mathematics. I have nothing to say except worship."

"Biqi, is our Teacher Gu really that strong?"

"That's right!" Bi Qi held her head high, feeling proud of herself.

If Teacher Gu wasn't so strong, how could he take Teacher Gu as his goal?

"Now you should believe that Teacher Gu is capable of teaching us mathematical analysis, right?" Bi Qi said with a smile.

"It's indeed much more reliable than before." Zhang Zhenzhen nodded with deep approval, "Before, I had no idea at all."

"But before Teacher Gu actually lectures, I still have doubts." Zhang Zhenzhen added.

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

…………

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

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

But Yanda is different.

The textbooks for most courses in the Department of Mathematics are basically textbooks published by Yanda Press.

The course "Mathematical Analysis" is no exception.

In the Department of Mathematics at Yanda, the textbook for mathematical analysis is a yellow-covered book compiled by teacher Wu Shengjian.

There are three volumes in total, one book per semester, and it can be completed in three semesters.

Gu Lu is currently responsible for teaching the book "Mathematical Analysis (1)".

He glanced at the audience and raised the textbook in his hand.

"Any students who have previewed this course during the summer vacation, please raise your hands?" Gu Lu asked slowly.

Swish, swish, swish!

Forty-five students raised their hands in unison.

"Not bad." Gu Lu nodded with satisfaction and then asked, "After finishing the preview, each student will raise his hand."

There were only about twenty people left raising their hands.

"Students who have finished previewing the books Number One and Number Two raise their hands."

Only seven or eight people raised their hands.

"Students who have finished previewing all three books, counting one, two, three?"

This time, only three people raised their hands.

Sitting in the front row were Bi Qi and Ma Zhengxuan, as well as the only female student in the class sitting in the back row.

Gu Lu's eyes fell on the girl in the last row.

"Classmate, what's your name?"

"Teacher, my name is Bai Yao." Bai Yao stood up and suddenly stared at Gu Lu with her moving eyes.

Bai Yao!

Hearing this name, Gu Lu was still calm, but the other students in the class were not calm yet.

Bi Qi glanced at Zhang Zhenzhen, who had a surprised look on his face, and asked, "Why, do you know this person?"

Zhang Zhenzhen shook his head, "I don't know him, but I have heard his name for a long time."

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

Another top scorer in the college entrance examination?

Bi Qi turned around and glanced at Bai Yao in the back row, his eyes deep.

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

But their mathematics department includes two of them.

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

Plus a few recommended students.

This year’s Department of Mathematics at YSU can be described as full of talents.

On the stage, Gu Lu picked up a piece of chalk and said with a smile, "It's the first class today. Before I lecture, let me check your preview results."

"I will put a few questions on the blackboard later for you to answer. The questions will be answered in a rush-answer format. There will be no penalty for wrong answers, but there will be rewards for correct answers."

"In your mathematical analysis of the final grade of this course, the final exam grade accounts for 80% and the usual grades account for 20%. What is the measurement standard for daily grades? One is attendance, and the other is class performance."

"I don't know what other teachers are like, but this is how I set it up. The usual score is based on a hundred-point system. Five points will be added to the class performance, five points will be deducted for being late, and ten points will be deducted for being absent from class. So, we, you guys from the mathematics department,

Students should know very well.”

"Next, I'll start asking questions."

After saying that, Gu Lu turned around and scribbled the title on the blackboard.

Since it is to test the results of pre-study, the difficulty of the questions will definitely not be too high.

Gu Lu came up with four questions based on the principle of starting from difficult to easy.

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

[2. Suppose f(x)∈c[a,b], f(a)=f(b), prove: there is a sequence xn that satisfies xn＜yn,lim:n→∞(yn-xn)=0,

And f(xn)=f(yn).】

【3. Prove that ∑:n,k=0(-1)^kc:kn(1/1km)=∑:m,k=0(-1)^kc:km(1/1kn).】

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

Four questions, gradually increasing in difficulty.

Gu Lu wrote the four questions on the four blackboards respectively, then turned around and looked at the people below, "For the first question, who is coming?"

"Teacher, me!"

"Teacher, let me go."

"Teacher, please turn over my sign!"

Many people below raised their hands.

The first question is the easiest of the four questions, so it is naturally competed by many people.

However, a few people did not raise their hands.

For example, Bi Qi and the others are sitting in the first row, and Bai Yao is sitting in the back.

It's not that they can't.

It's that they don't bother to do such a simple question, so they give the opportunity to others.

"Come on, let's take this chubby classmate." Gu Lu turned over the sign of a chubby boy. After asking his name, he handed him a piece of chalk and extended his hand to indicate for him to answer the question.

When it came to the second question, there were far fewer students raising their hands.

Gu Lu ordered a boy sitting in the second row.

For the third question, not many people raised their hands.

Most students were writing and drawing on paper while frowning and thinking about problem-solving ideas.

Although Gu Lu said there is no penalty for wrong answers.

But if you go up unprepared and fail to do it, wouldn’t it be embarrassing to be watched by more than 40 classmates below?

"Zhengxuan, is it okay?" Gu Lu handed the chalk to Ma Zhengxuan, who was in the first row.

"no problem."

Ma Zhengxuan stood up and walked to the podium unhurriedly. He almost didn't have time to think, so he wrote the formula with chalk on the blackboard.

【1/1km=∫(1,0)x^(km)dx,

∑:n,k=0(-1)^kc:kn(1/1km)=∫(1,0)∑:n,k=0(-1)^kc:knx^(km)dx=∫(

1,0)x^m(1-x)^ndx.

The same can be said...]

Ma Zhengxuan writes very smoothly.

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

Many classmates looked at Gu Lu and lowered their heads in fear.

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

That's Taylor's formula!

In the entire mathematical analysis course, it is listed as one of the most difficult contents to understand.

Moreover, the set of questions proposed by Teacher Gu seems to be not only a simple transformation of Taylor's formula, but also... more complicated.

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

But now, it is left to them, the freshmen who have just entered school.

How could anyone do that?

But at the moment when everyone's idea appeared, two hands were raised at the same time, almost in no particular order.
Chapter completed!