After a thousand years of trading, start a million barrels of oil

Chapter 52 Please Answer

"Ah~" Jiang Fan drank half of the water, and when he saw the professor pointing at him, he also looked puzzled.
Why are there so many people in this classroom, why did they click on me?
But I am not a student of your school, not even a college student.

But out of politeness, he hastily put down the water glass and stood up.

The most tangled person at the moment is actually Lin Wan. She thought she was done for, she must have been chatting with Jiang Fan just now and was noticed by the professor.

She knows the habits of some college teachers, some people don't care about anything, you play with you, I will fall down after my class,
But there are also some teachers who are more rigorous and responsible, and sometimes they just like to ask students who don't listen carefully to answer questions.

The professor in front of him, judging from his rigorous teaching style and the experience of listening to his lectures a few times before, definitely belongs to the latter.

And today, it was rare for Brother Fan to accompany her to class, and the chat was so happy that he just forgot about the professor.
Lin Wan felt so regretful,

Brother Fan never went to college at all, and he has been working for so many years. How can he know anything about Fourier series? It would be nice if he could remember the multivariate equations in high school and be able to solve them.

No, I have to help Brother Fan.

In fact, Lin Wan can't remember what the concept of Fourier series is. She didn't quite understand it when she was a freshman.

After another year of primary school, it was returned to the teacher early,

So she hurriedly borrowed a book from a classmate next to her, found the concept, and wanted to tell Jiang Fan in a low voice,

But this series of actions could not escape the professor's eyes, he was staring at both of them,
So before Lin Wan could speak, the professor called by name and said, "Don't remind the female students next to you."

Alright~, now I can't talk anymore,

Lin Wan just suffocated there, there was nothing left to do,

I had to look at Jiang Fan cautiously and a little bit embarrassed, meaning Brother Fan, you can only rely on yourself,

Or if you admit a mistake, just say that you didn't listen well, and we just don't talk later.

Jiang Fan is not panicking at all at the moment, this question is very simple,

Goldbach guesses I won't, isn't the concept of a Fourier series not too easy?

Jiang Fan mobilized the knowledge in the knowledge patch through his brain, because he had an overview before, and the system catalog and so on were still in his mind, so he quickly found the corresponding knowledge points.

So he said to the professor: "The core concept of Fourier series is: any periodic function can be expressed by an infinite series composed of sine and cosine functions."

It is indeed very simple in concept, but this simple transformation has great significance in practical application.

However, Jiang Fan's answer surprised Lin Wan. She looked at Jiang Fan in surprise,

I don’t know how this brother Fan who has never been to college can answer the concept of Fourier series so easily.

Although it's really not complicated, Brother Fan has never learned it, how did he do it?

The professor nodded slightly. Of course he also knew that the concept was very simple, but this was just an introduction, and his questions would not stop here.
The professor then asked: "Actually, what I want to ask is, what is the generalized concept of Fourier series?"

This question is a bit beyond the outline. There is no discussion of generalized Fourier series in textbooks.
Unless you read extracurricular books by yourself, it is generally difficult to answer.

But the purpose of the professor is to make him unable to answer, and let him understand that there are still many things you don't know. Don't just understand two concepts and then get up to the sky.

But this question is not a problem for Jiang Fan. He has a reserve of knowledge from mathematics majors all the way to Ph.D.
Jiang Fan brain searched the relevant content in the knowledge patch, and calmly replied:

"The generalized Fourier series is actually similar to the orthogonal decomposition of vectors in geometric space.

The Fourier series of a periodic function is an orthogonal decomposition of the function on the inner product space, and its orthogonal decomposition is extended from the {ek=eikx, k∈} basis to the Legendre polynomial and Haar wavelet basis, etc., which is called the generalized Fourier Leaf series.

Of course, if expressed in formulas,

For a function f(x) with second-order continuous derivatives defined on the interval [-1, 1], when it has the same boundary conditions as P, (z), it can be expanded to be absolute and consistent according to Pl(x) convergent series,

f(x)=ΣflPl(x),

This is called a generalized Fourier series. "

Jiang Fan gave a comprehensive answer directly from the level of understanding and formula.

Lin Wan was dumbfounded. When Jiang Fan answered, she was also flipping through the book, and she found that there was no concept of generalized Fourier series in the textbook.

It was obvious that the professor was embarrassing Jiang Fan. Lin Wan was thinking that if Brother Fan couldn't answer, he could just sit down. It wouldn't be shameful if he had already answered one question.

As a result, people directly answered the answer to the second question,
Is this still the Brother Fan I know?
The professor is also a little surprised, super-syllabus questions are also available, have you learned extracurricular books for high mathematics?
The students in other classrooms were also whispering in surprise, but they were not surprised by Jiang Fan's answer,
But who is this person?I haven't seen it before, let's take a class.

But the professor didn't intend to let Jiang Fan go so easily. After all, he was talking in private first, and the phone was not on silent to disrupt the classroom order.

Then I ran out to make a phone call during class, and woke up with 'Hi~' before I went out.

If you violate classroom discipline three times in a row, then I will give you 3 questions accordingly.

Answering the first two questions correctly is considered good, but you can try the last one.

The professor directly skipped the college-level test questions related to Fourier series, and found a question he gave to his graduate students in the mathematics department two days ago.
The questions not only need to apply the knowledge of Fourier series, but also use precise integrals, linear time-varying systems and periodic Riccati differential equations.

It can be regarded as a lot of super-class ones, and his graduate students who were in the first year of research did not make it, and the ones in the third year of research finally managed to make [-] to [-]%, and the level of doctoral one is more stable.

However, his intention is to play an educational role, so the difficulty is not the main consideration.

After the professor found the topic, he directly typed it on the projection screen through the computer:

'Please combine the Fourier series expansion method, based on the time-varying fine integral, to solve the efficient algorithm for the periodic coefficient Riccati differential equation, specifically.'

The professor displayed the problem on the projection screen and said to Jiang Fan, "Let's solve this problem."

Before Jiang Fan moved, all the students were dumbfounded.

(End of this chapter)