The Science Fiction World of Xueba

Pang Xuelin's tone of voice was unhurried, and he spoke fluent Mandarin, as standard as a TV announcer. When it came to English names, he also spoke authentic American English.

The tattered clothes did not conceal his aura at all. On the contrary, in every move, there was a faint top-level scholarly demeanor that impressed all the audience.

The classroom gradually became quiet, leaving only Pang Xuelin's voice echoing in the air.

"Fredholm, Hilbert's work on integral equations, we can start from the following two specific examples. The earliest source of integral equations is Fourier's research on thermal problems. In 1822, Fourier discussed how to solve the following equation inversely: f(x)=∫ Re^itxg(t)dt, that is, knowing f, how to find g. In modern language, this is actually the inverse transform of Fourier transform..."

"Secondly, when studying second-order ordinary differential equations, it is found that they are equivalent to a class of integral equations. For example, the solution f"(x)+g(x)=f(x) of the equation. If the boundary conditions f(a)=1 and f'(a)=0 are satisfied, the basic solution of this equation can be used to prove that the solution of the equation satisfies..."

"The integral equations exemplified above can be classified into the following two forms: ∫K(x, y)f(y)dy=g(x); f(x)-K(x, y)f(y) dy=g(x). The first person who gave a strict treatment method for these two types of equations was Fredholm, a Swedish mathematician. He published a series of articles between 1900 and 1903 and gave a solution. I Here is a brief discussion of the modern version that his thought finally evolved into: that is, Fredholm's two is one principle. If K(x, y) is a certain type of regular symmetric kernel..."

...

Wang Chongqing, who was on the side, was stunned. He never thought that the course of functional analysis could be taught in this way.

In particular, Pang Xuelin combined the development history of functional analysis with various theorems and concepts during his lectures, which did not sound boring at all, but gave people a refreshing feeling.

Even Wang Chongqing himself is not very clear about many of the cases that Pang Xuelin mentioned.

In this era, students who can be admitted to Lincheng University have good foundations.

In addition, they have already studied the basic course of functional analysis for one semester, and they are not unfamiliar with various conceptual theorems.

Pang Xuelin deduced some concepts by explaining the history of mathematics. In this way, those originally abstract concepts and theorems suddenly became vivid and interesting.

"Damn it,

It turned out to be like this..."

"Why do I feel that he speaks better than Professor Wang? I was a little ignorant of the Hahn-Banach theorem that Professor Wang said before, but now I understand how the theorem came about after he said it... "

"Which class does this guy belong to? I didn't expect that there are such great people in our school..."

"Tell me, does this guy look like the floor-sweeping monk in Tianlong Babu? He looks like an ordinary person, but he is actually a real expert..."

...

The students in the audience chattered.

Don't be afraid of not knowing the goods, but be afraid of comparing goods.

Pang Xuelin's explanation, like a catalyst, straightened out everyone's thinking at once.

Even Wang Chongqing himself, because of Pang Xuelin's explanation, has a deeper understanding of the course of functional analysis.

Time passed by, and before you knew it, the bell rang for the end of get out of class. At this time, Pang Xuelin had spoken for less than a third of the time.

Pang Xuelin turned his gaze to Wang Chongqing and said, "It's time for get out of class to end, why don't you come here first today."

Wang Chongqing smiled, looked at the watch on his wrist, and said, "Students, did this student speak well?"

"good!"

In the classroom, everyone shouted in unison.

Wang Chongqing said: "It's 11:30 noon, and the morning class is over. This student, can you see if this is okay? You can continue to lecture and finish what you want to talk about. As for the students here, if you want to continue Those who are attending the class can stay and continue to listen, and if you don’t want to listen, you can also leave, but please try to keep quiet so as not to disturb this classmate’s lecture.”

"Great, you can continue to listen!"

"I agree!"

"Professor Wang's suggestion is good! I was not sure about functional analysis, but after listening to this student's explanation, I think I have at least 70% certainty to pass the final exam."

"Yes, this classmate gave a very good lecture. I feel that my understanding of most of the content of functional analysis has been deepened."

...

Pang Xuelin didn't expect the bald professor's proposal to attract so many people's consent, so he smiled and said, "Okay, then I'll continue."

The whole classroom fell silent again, except for a few people, most of the students stayed behind.

It was not until one o'clock in the afternoon that Pang Xuelin roughly explained the part of linear functional analysis.

"Okay, I will stop here for the entire linear functional analysis part, and finally I will talk about the learning method of functional analysis. I will give you the following two suggestions.

First, the idea must be specific.

Analysis becomes more abstract in the later stage. Many people save themselves by using images, but the disadvantage of this method is that it is easy to lead themselves into the ditch, because there are a lot of counter-intuitive examples in analysis, and relying too much on images will make them do things later. Overturning the problem: because you will mistakenly think that a certain result is correct, and then get stuck there. The best way to do this is with specific examples. Memorizing and understanding theorems with concrete examples is a very important step, but one that is clearly overlooked by many people.

Second, we must integrate theory with practice. Analysis, especially the theory of functional analysis is essentially a summary, which is summarized from many specific applications. The biggest piece is partial differential equations, so almost everyone who works on partial differential equations is not bad at learning functionals. It is not without exaggeration to say that every functional concept in textbooks corresponds to an application. It is natural for many people to be empty-headed after learning functional theory, because you don't know what these concepts are useful for. The application of finite dimensions is not enough, and only infinite dimensions are meaningful. "

"Okay, today's explanation on functional analysis ends here first, thank you everyone!"

The voice fell, and the classroom was quiet for a while.

clap clap...

Wang Chongqing, who was sitting in a corner, stood up and applauded first. Then, the applause swept across the lecture hall from front to back like thunder.

Wang Chongqing stepped forward and said with a smile, "Student, which class are you in? I didn't expect talents like you to be hidden in our school."

Pang Xuelin said with a smile: "Professor Wang, I'm not a student in the Department of Mathematics. After all, we are colleagues..."

He already knew the professor's last name from the student's address just now.

"Oh, are you a new teacher in our mathematics department?"

Wang Chongqing was slightly taken aback.

Pang Xuelin shook his head, smiled and stretched out his hand and said, "No, Professor Wang, let's get to know each other again. I'm Pang Xuelin, a primary school teacher in Lingziding Village, Dayu Township, Anhe County, G Province!"

In an instant, the originally noisy classroom could be heard quietly.

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