Pang Xuelin's tone is not bad, fluent Mandarin, like the standard of a television announcer, when speaking English names, it is also authentic American English.

His tattered clothes didn't hide his temperament, but in the midst of every move, there was a faint scholarly style that made all listeners convinced.

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

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

"Second, when studying the second-order ordinary differential equations, they are equivalent to a class of integral equations. For example, the solution of the equation f" (x) + g (x) = f (x). If the boundary conditions f (a) = 1 and f \ '(a) = 0 are satisfied, it can be proved 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 rigorous approach to these two types of equations was the Swedish mathematician Fredholm, who published a series of articles between 1900-1903 giving a solution. I Here is a brief discussion of the modern version of his idea: the Fredholm principle of two rules and one. If K (x, y) is some kind of regular symmetric kernel ... "

Uh ...

Wang Chongqing, who was aside, was stunned. He never thought that this course of functional analysis could still be told like this.

Especially when Pang Xuelin combined the development history of functional analysis with various theorems and concepts during the lecture, it didn't sound boring at all, but gave people a refreshing feeling.

He even didn't know much about Wang Chongqing himself about many examples of Pang Xuelin.

In this era, the students who can be admitted to Lincheng University have a good foundation.

加上 Coupled with the one-semester basic functional analysis course, they are also familiar with various concept theorems.

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

"Oh, that's it ..."

"How do I feel that he speaks better than Professor Wang? The Hahn-Banach theorem that Professor Wang said was a bit unknowing before, and now I heard him say how the theorem came, I knew it all at once ... "

"Which class is this guy? I didn't expect that there are such bulls in our school ..."

"You said, this guy doesn't look like a sweeping monk in Tianlong Babu. It looks unattractive and is no different from ordinary people, but in fact it is a true master ..."

Uh ...

The students on the stage talked a lot.

I am not afraid of not knowing the goods, I am afraid of comparing goods.

Xi Pang Xuelin's explanation seemed like a catalyst to straighten out everyone's thinking.

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

The time elapsed minute by minute. Unconsciously, the bell rang after class. At this time, Pang Xuelin spoke less than one-third.

Xi Pang Xuelin turned his eyes to Wang Chongqing and said, "It's time to go to class. If not today, let's get here first."

Wang Chongqing smiled, looked at his wrist watch, and said, "Classmates, is this classmate speaking well?"

"it is good!"

In the classroom, everyone shouted in unison.

Wang Chongqing said: "It's 11:30 noon, the morning class is over. This classmate, you can see how this works. You can continue to lecture and finish what you want to say. As for the classmates here, if you want to continue If you listen, you can stay and listen. If you do n’t want to listen, you can also leave, but please try to keep quiet so as not to affect the student ’s lecture. "

"Great, you can keep listening!"

"I agree!"

"Professor Wang's proposal is good! I didn't know the functional analysis at first. As a result, after listening to this classmate's explanation, I think I have at least 70% certainty to pass the final exam."

"Yes, this classmate spoke very well. I feel that my understanding of most of functional analysis has deepened."

Uh ...

Xi Pang Xuelin did not expect that this balding professor's proposal would cause so many people to agree, so he laughed and said, "OK, I will continue to talk."

The whole classroom was quiet again, except for a few people, most of the students stayed.

It was not until 1 pm that Pang Xuelin gave a rough explanation of the linear functional analysis.

"Well, I will talk about the entire linear functional analysis part first, and finally I will talk about the learning method of functional analysis. I give you the following two suggestions.

First, the idea must be specific.

The more the analysis becomes more and more abstract in the later period, the method that many people save is the image. Roll over when you have a problem: because you will mistakenly think that a certain result is right, and then get stuck there. The best way is a concrete example. It is a very important step to memorize and understand theorems with specific examples, but it is clear that many people ignore this.

Second, we must combine theory with practice. The theory of analysis, especially functional analysis, is essentially a summary, which is summarized from many specific applications. The largest piece is a partial differential equation, so almost functional studies of partial differential equations are not bad. It is no exaggeration to say that each functional concept in the textbook corresponds to an application. Many people's minds are natural after learning functional theory, because you don't know what these concepts are useful. The application of finite dimensions is not enough. Only infinite dimensions are meaningful. "

好 "Well, today's explanation of functional analysis will come here first, thank you all!"

My voice dropped, and the classroom was quiet for a little while.

Crackling ...

崇 Wang Chongqing, who was sitting in a corner, took the lead to applaud ~ lightnovelpub.net ~ Then, applause swept through the entire staircase classroom like thunder.

Wang Chongqing stepped forward and said with a smile: "This classmate, which class are you from? I did not expect that our school still has talents like you."

Pang Xuelin laughed: "Professor Wang, I'm not a student in the Department of Mathematics. It really counts, we are two colleagues ..."

Just now he already knew the professor's last name from the student's title.

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

Wang Chongqing for a moment.

She Pang Xuelin shook her head and stretched out her hands with a smile: "No, Professor Wang, get to know me again. I am a teacher at Lingziding Village Elementary School, Datong Township, Anhe County, G Province, Pang Xuelin!"

For a moment, the noisy classroom was quietly heard.

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