The first lesson, mathematical analysis.

In this class, not only Chen Zhou and his mathematics department, but also students from two other departments attended the class together.

This class is taught by Professor Wu, who has rich teaching experience in the School of Mathematics.

Professor Wu sorted out his black-framed glasses, first introduced himself, and then said: "You don't need to be restrained in my class, you can completely let go. You can listen to the class, learn by yourself, or read other things.

I don’t make any discipline requirements for books.”

The students were overjoyed when they heard this.

Professor Wu glanced at the happy students, and he continued with some difficulty saying: "Of course, I have a prerequisite. No matter what you do, you must ensure that you keep up with the course progress. Then, before each class is over

, I will give you a number of questions based on the course progress and test your learning situation in class."

Well, it turns out that the previous words are all lies, and that's the point.

Sorrow always comes so quickly, especially when you are happy.

Some students began to whisper to Professor Wu, but Professor Wu didn't care at all.

Next, Professor Wu picked up the textbook in his hand and said, "This textbook for numbering was compiled by Professor Yan Dawu. It has been used in our Yan Da University for several years, and the teaching effect is pretty good."

"Mathematical analysis is one of the most important basic mathematics courses. It is an important foundation for your subsequent courses and your future work in the field of mathematics. So, I hope you can understand it thoroughly."

Chen Zhou took a look at this yellow-skinned "Mathematical Analysis" (Volume 1), which is what you need to learn this semester.

There are also volumes 2 and 3, which will be completed in the next two semesters.

"Mathematical Analysis" (Volume 1) has six chapters, including the limits of functions, sequences, limits and continuity of functions, derivatives and differentials, application of derivatives, and indefinite integrals.

Chen Zhou glanced at the catalogue and a smile appeared on the corner of his mouth.

Chen Zhou was originally worried because the system was activated and he had not filled out his application when he chose the self-study task of high mathematics for the first time.

After filling out the application and receiving the admission letter from Yan University's Department of Mathematics, he logged into the student system and checked the courses in the Department of Mathematics, but there was no such course in advanced mathematics at all.

Chen Zhou was confused for a moment and even suspected that the sand sculpture system was cheating on him again.

However, the system gave him a comforting sentence: "Knowledge is interoperable."

Although he doubted this sentence, he still completed the task and could not be stuck in the task.

But now, after seeing the content of this book, he felt that the saying that knowledge is interoperable has no problem at all.

Well, that's right, these contents are already familiar with each other in the high school.

If they were not familiar with each other, Chen Zhou believed that they would be able to mature sooner than the original knowledge.

Chen Zhou retracted his thoughts and heard Professor Wu’s voice: “What is mathematical analysis? Mathematical analysis, also known as advanced calculus, is the oldest and most basic branch of analysis.”

"The main content of mathematical analysis is calculus. The theoretical basis of calculus is limit theory, and the theoretical basis of limit theory is real number theory."

"Students, do you know what is the most important feature of the real number system?" Professor Wu asked and answered, "The most important feature of the real number system is continuity. With the continuity of real numbers, you can discuss limits, continuity, and differentials.

and integral. It is in the process of discussing the legitimacy of various limit operations of functions that people gradually establish a rigorous mathematical analysis theoretical system.”

"Now, everyone understands the origin of the number scores, and we will officially start class." Professor Wu said, slowly opening the textbook.

Chen Zhou thought it was OK. Who said that university teachers were very fast in teaching? Isn’t the popular science before this class considerate?

However, Professor Wu's next words seemed to be to answer Chen Zhou's doubts.

Professor Wu said: "First turn to page 4, starting from the last paragraph, I will tell you about the Dede King division. This point is more important and must be thoroughly understood."

"Professor Wu, where is the previous content?" someone interrupted.

Professor Wu glanced at the man and replied lightly: "Do I have to tell you about the gathering? Just review it if you want to."

Then he continued to give a lecture: "Before I talk about the Dedekin division theorem, I need to talk about the Dedekin division first..."

"...... Then Dedekin divides any theorem of r (a∣b), and there must be a minimum number in b."

"...Bornated sets and definite boundaries are both conceptual. You can see them yourself, so I won't talk about them."

"... There are also ways to prove several commonly used inequalities, which are relatively simple, please see it yourself."

"Then talk about the functions below..."

Chen Zhou looked at Professor Wu who was talking on the podium speechlessly. Is this a lecture? It is faster than his reading...

Soon, the first chapter ended, and Professor Wu began to talk about the second chapter, the limits of the sequence.

Chen Zhou couldn't help but sigh, fortunately he finished studying his advanced mathematics, otherwise he would really doubt whether he could keep up with the progress.

The Dedekin division and Dedekin division theorem are not easy to understand.

However, Chen Zhou found that Zhao Qiqi and Zhu Mingli's eyes were shining, and he listened with relish.

Li Li, the fourth person in the dormitory, was also reading a book by herself.

"It turns out that playing games is an illusion..." Chen Zhou said in his heart, and then looked around the other students in the class.

Except for a few people, it is obvious that they cannot keep up with the progress. Most of the students are either listening to the class attentively or studying by themselves.

With twenty minutes left before get out of class, Professor Wu stopped and took a sip of water, and said, "Let's talk about that much today, the progress is a little slow. Next, is the time for answering questions in this class."

After saying that, Professor Wu turned around and started writing questions on the blackboard.

Chen Zhou flipped through the book and said that the yellow skin's number-point textbook had already been discussed for two chapters. Is this progress slow?

After proposing the question on the blackboard, Professor Wu turned around and said to everyone: "Everyone finds the draft paper and writes the name and answers. If not, just write the name."

Chen Zhou first took out the draft paper, wrote the name on it, then looked up at the blackboard, and copied the title on the draft paper.

"Suppose xn=(1((-1)^n)/n)^n,n=1,2,3..., try to prove that {xn} is a divergent sequence."

The question was very short, Chen Zhou only took a look and finished reviewing the question.

Professor Wu still didn’t make things difficult for everyone in the first class, and this question is not difficult.

Chen Zhou wrote:

"Proof: Because k→∞lim(1((-1)^2k)/2k)^2k=e"

"And k→∞lim(1((-1)^(2k1))/(2k1))^(2k1)=k→∞lim[1/(11/2k)^2k1)]·[1/(

11/2k)]=1/e”

"So n→∞limxn does not exist."

"Certify that {xn} is a divergent sequence."

The proof process is also very simple, mainly using the basic theorem of continuity of real numbers.

Chen Zhou checked it and there was no problem, so he got up and prepared to hand over the draft paper to Professor Wu.

Chen Zhou noticed that there were still more than a dozen people left in the classroom at this time.

And the three brothers in his dormitory have already left.
Chapter completed!