Xueba starts with change

Chapter 91 Lessons

The first class, Mathematical Analysis.

In this class, not only Chen Zhou and his Department of Mathematics, but also students from two other departments took the class together.

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

Professor Wu sorted out his black-rimmed glasses, introduced himself first, and then said: "You don't need to be restrained in my class, you can completely let go. You can listen to the class, study by yourself, or watch other Books, I don't make disciplinary requirements."

Hearing this, the students were overjoyed.

Professor Wu glanced at the happy students, and he continued unbearably: "Of course, I have a prerequisite. No matter what you do, you must ensure that you keep up with the progress of the course. Then, before the end of each get out of class , I will give a fractional question according to the progress of the course, and test your learning situation in class."

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

Sadness always comes so quickly, especially when you are joyful.

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

Next, Professor Wu picked up the teaching material in his hand and said, "This teaching material for numeracy was written by our Professor Yan Dawu. We have used it for several sessions at Yanda University, and the teaching effect is not bad."

"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. Therefore, I hope you will understand it thoroughly."

Chen Zhou glanced at the yellow-skinned "Mathematical Analysis" (Volume [-]), which he needed to learn this semester.

There are also Volumes [-] and [-], which are completed in the next two semesters.

"Mathematical Analysis" (Volume [-]) has six chapters, covering functions, limits of sequences, limits and continuity of functions, derivatives and differentials, applications 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 of the activation of the system, when he chose the self-study task of advanced mathematics for the first time, he hadn't filled in the volunteers.

After filling out the application and receiving the admission letter from the Department of Mathematics of Yan University, he logged into the student system and inquired about the courses of the Department of Mathematics, but it turned out that there was no advanced mathematics course at all.

Chen Zhou was stunned for a moment, and even suspected that the sand sculpture system was tricking him again.

However, the system gave him a word of comfort: "Knowledge is interoperable."

Although he doubted this sentence, he still completed the task and 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 saying that knowledge is interoperable.

Well, yes, these contents are already familiar in the high school.

For those who are not familiar with it, Chen Zhou believes that they will soon 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 limit theory, and the theoretical basis of limit theory is real number theory."

"Then students, do you know what the most important feature of the real number system is?" Professor Wu asked and answered, "The most important feature of the real number system is continuity. Only with the continuity of real numbers can we discuss limits, continuity, and differentiation. And integral. It is in the process of discussing the legality of various limit operations of functions that people gradually establish a rigorous mathematical analysis theoretical system."

"Then now, everyone understands the origin of the score, and we are officially in class." After Professor Wu finished speaking, he slowly opened the textbook.

Chen Zhou thinks it's okay, who said that university teachers teach fast?Isn't the science before this class not considerate?
However, Professor Wu's next words seemed to be to answer Chen Zhou's doubts.

Professor Wu said: "Turn to page 4 first, starting from the last paragraph, I will 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 by raising his hand.

Professor Wu glanced at the man and replied lightly: "Do you still need me to tell you about the collection? Just review it if you want to see it."

Then he continued his lecture: "Before I talk about Dedekind's division theorem, I need to talk about Dedekind's division first."

".Then for any partition of R (A∣B) by Dedekind's theorem, there must be a minimum number in B."

"The bounded set and the real world are both conceptual. You can see for yourself, and I won't talk about it."

". Several commonly used inequalities also have proof methods, which are relatively simple. See for yourself."

"Then let's talk about functions"

Chen Zhou looked at Professor Wu, who was talking on the podium, speechless. Is this a lecture?It's faster than he flips through the book.
Soon, Chapter 1 ended, and Professor Wu began to talk about Chapter 2, the limit of the sequence.

Chen Zhou couldn't help but sighed with emotion. Fortunately, he had completed the self-study of advanced mathematics, otherwise he really doubted whether he could keep up with the progress.

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

However, Chen Zhou found that Zhao Qiqi and Zhu Mingli both had sparkling eyes and listened with relish.

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

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

Except for a very small number of people, it was obvious that they could not keep up with the progress. Most of the students were either listening to the lectures attentively, or bowing their heads and studying by themselves.

With 10 minutes left before the end of get out of class, Professor Wu stopped to take a sip of water, and then said, "Let's talk so much today, and the progress is a bit slow. Next, it's time to answer questions for this class."

After speaking, Professor Wu turned around and started writing the topic on the blackboard.

Chen Zhou flipped through the book. The yellow-skinned fractional textbook has already covered two chapters. Is this progress considered slow?

After Professor Wu finished the question on the blackboard, he turned around and said to everyone: "Everyone finds a scratch paper and writes their name and answer. If not, just write their 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.

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

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

In the first class, Professor Wu still didn't embarrass everyone too much. This question is really not difficult.

Chen Zhou wrote:

“证明：由于k→+∞lim(1+((-1)^2k)/2k)^2k=e”

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

"Therefore n→∞limXn does not exist."

"It is proved that {Xn} is a divergent sequence."

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

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

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

And the three brothers in his dormitory have long since left.

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

(End of this chapter)