Lesson 1, Mathematical Analysis.

In this class, not only Chen Zhou's mathematics department, but also students from two other departments were in class together.

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

Professor Wu tidied up his black-framed glasses, introduced himself first, and then said, "You don't need to be restrained when you take my class, you can completely let go." You can listen to lectures, you can study on your own, you can read other books, and I don't have any discipline requirements. ”

Hearing this, the students were overjoyed.

Professor Wu glanced at the happy students, and he continued with some reluctance: "Of course, I have a prerequisite. Whatever you do, you have to make sure that one thing is to keep up with the course. Then, before the end of each class, I will come up with a question with a few points according to the progress of the class, and test your learning in class. ”

Well, the words in front of the dare are all lies, and that's the point.

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

Some of the students began to whisper complaints about Professor Wu, but Professor Wu did not care.

Next, Professor Wu picked up the textbook in his hand and said: "This textbook was compiled by Professor Yan Dawu, and it has been used in our Yan University for several sessions, and the teaching effect is not bad. ”

"Mathematical analysis is one of the most important mathematics foundation courses, and it is an important foundation for your subsequent courses and future work in the field of mathematics. So, I want you to eat it thoroughly. ”

Chen Zhou glanced at the yellow-skinned "Mathematical Analysis" (Volume 1), which needs to be learned this semester.

There are also books 2 and 3, which are completed in the next two semesters.

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

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

Originally, Chen Zhou was a little worried, because the system was activated, and when he chose the self-study task of high mathematics for the first time, he had not yet filled in the volunteers.

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

Chen Zhou was stunned for a moment at that time, and even suspected that the sand sculpture system was cheating on himself again.

It's just that the system gave him a comforting word: "Knowledge is interconnected." ”

Although he doubted this sentence, he still completed the task, and he couldn't be stuck by the task.

But now, after reading the content of this book, he feels that there is nothing wrong with the sentence that knowledge is interconnected.

Well, that's right, these contents are already familiar in the high numbers.

Unmixed, Chen Zhou believes that soon they will be more familiar 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 the limit theory, and the theoretical basis of the limit theory is the theory of real numbers. ”

"Then students, do you know what is the most important feature of the real number system?" Professor Wu asked himself, "The most important feature of the real number system is continuity, and with the continuity of real numbers, we can discuss limits, continuity, differentiation and integration. It is in the process of discussing the legitimacy of various limit operations of functions that a rigorous theoretical system of mathematical analysis has been gradually established. ”

"Now, everyone knows the origin of the number of points, and we officially start classes. After Professor Wu finished speaking, he slowly opened the textbook.

Chen Zhou thinks it's okay, who said that university teachers are fast in their lectures? Isn't this pre-class science popularization intimate?

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

Professor Wu said: "Let's turn to page 4 first, and from the last paragraph, I'll tell you about the Dedekind division. This point is more important and must be thoroughly understood. ”

"Professor Wu, what about the previous content?" someone interrupted with a raised hand.

Professor Wu glanced at this person and replied lightly: "Do you still need me to tell you about the gathering? ”

Then he continued the lecture: "Before I talk about the Dedekind division theorem, I need to talk about the Dedekind division ......"

“...... Then Dedekind's separation theorem must have a minimum number in B for any division of R (A∣B). ”

“...... Bounded set and definite boundary, both of which are conceptual, and I will not talk about them if you see for yourselves. ”

“...... There are also proof methods for several commonly used inequalities, which are relatively simple, and look at them for yourself. ”

"So let's talk about the function ......"

Chen Zhou looked at Professor Wu on the podium a little speechlessly, is this a lecture? This is faster than he flips through a book...

Soon, the first chapter ended, and Professor Wu began to talk about the second chapter, The Limits of Sequence.

Chen Zhou couldn't help but sigh with emotion, fortunately he had finished self-learning in high mathematics, otherwise he really doubted that he could keep up with the progress.

The Dedekind division and the Dedekind division theorem are not easy to understand.

It's just that Chen Zhou found that Zhao Qiqi and Zhu Mingli's eyes were shining and they listened with relish.

Li Li, the fourth person in the bedroom, was also reading by himself.

"Sure enough, playing games is all an illusion..."Chen Zhou said silently in his heart, and then looked at the other students in the class.

Except for a very few people, it can be clearly seen that they can't keep up with the progress, and most of the students are either listening attentively or bowing their heads and studying on their own.

Twenty minutes before the end of class, Professor Wu stopped to take a sip of water, and then said, "Let's talk so much today, the progress is a little slow." Below, is the time for answering questions in this class. ”

After speaking, Professor Wu turned around and began to write the question on the blackboard.

Chen Zhou flipped through the book, and the yellow-skinned textbook had already taught two chapters, this progress was slow?

After writing the question on the blackboard, Professor Wu turned around and said, "Everyone finds their own scratch paper and writes their names and answers. If not, just write your name. ”

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

"Let Xn=(1+((-1)^n)/n)^n,n=1,2,3... , try to prove that {Xn} is a divergent sequence. ”

The topic was very short, Chen Zhou only glanced at it, and the review was completed.

Professor Wu didn't bother everyone too much in the first class, and this question was not difficult.

Chen Zhou wrote:

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

And k→+∞lim(1+((-1)^(2k+1))/(2k+1))^(2k+1)=k→+∞lim[1/((1+1/2k)^2k+1)]· [1/(1+1/2k)]=1/e”

"So n→∞limXn does not exist. ”

"It turns out that {Xn} is a divergent sequence. ”

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

Chen Zhou checked it and found no problem, so he got up and prepared to hand over the scratch 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 elder brothers in his bedroom have long since left.

Chen Zhou politely handed the scratch paper to Professor Wu and left the classroom.