Become a master from now on

Chapter 244 Fourier Series
Shen Lang's words expressed the charm of mathematics. Although many things can be calculated by computers, computers are always just computers, and the human brain is the most complicated calculation program.

Through the human brain, it is possible to break through the complicated and unsolved mathematical problems in the world one by one.

Even if it may be very long in time, it will be resolved one by one in the end.

"How is it? After watching it for a few days, is there anything you don't understand?"

Among beauties and mathematics, Shen Lang perfectly blends the two together, and does not delay anyone. When it comes to beauties, he is professional, and when it comes to mathematics, he is also knowledgeable. If Shen Lang was born in the Ming Dynasty, I am afraid Like Tang Bohu, he is generally a romantic talent. Of course, the premise is that the Ming Dynasty is equally good at mathematics, not literature.

When Fang Chao heard this, he immediately told what he had not understood in the past few days, hoping to get Shen Lang's guidance.

As far as Shen Lang can tell about Fang Chao's thirst for knowledge, he will not hesitate to teach him and is willing to share things. He has taken a fancy to Fang Chao's potential and regards him as his junior. He hopes that Fang Chao will excel in mathematics. The level can be greatly improved.

Chinese people can't say that there is little research in mathematics, but when it comes to professional fields, there are very few mathematical geniuses of the younger generation, and the older generation is unwilling to teach more, just throwing some templates and papers to You, let yourself figure it out.

How much you can comprehend depends on your personal ability.

After all, mathematics is not easy to teach, especially advanced mathematics. If you have no talent, even the teacher is unwilling to say a few words, which is too wasteful.

If you really have a certain talent in mathematics, considering Shen Lang's temperament, you really don't have to say a few words. His current approach is the same as that of some older professors, with a very high vision.

But Fang Chao is really an exception. For such a person, Shen Lang is trying every means to get Fang Chao to go to Qingbei University. If this is the case, he will be very happy to have such a junior and is willing to spend more time As for Fang Chao, no matter how much effort he puts into it, Fang Chao is still from the Northern Qing Dynasty...

But if Fang Chao decides to go to Peking University in the end, doesn't this mean that he is raising a tiger to be troubled?Create a powerful enemy for Qingbei?

But in the end, Shen Lang rejected this absurd idea. Qingbei and Peking University are all Chinese. Wouldn't it be good for the Chinese to have one more powerful mathematician?

What's more, Fang Chao's comprehension ability is so strong, just pointing out the other party's mathematics will greatly improve him, so why not do it?

So Fang Chao took out a piece of useless waste paper from the ground, then took out the hotel's ballpoint pen, and wrote a line of number symbols on it.

Assume two n-dimensional vectors, (X1, X2, X3...Xn), (Y1, Y2, Y3...Yn).

定义其内积，=X1·Y1+X2·Y2+X3·Y3+……Xn·Yn
"Now that we have the definitions, we can define two additional concepts, distance and orthogonality, defining the norm as...the corresponding distance can be defined as...two vectors X and Y are orthogonal if..."

While speaking, Fang Chao quickly wrote down a few formulas on the scratch paper.

|X|=√(X,X)

d(X,Y)=||XY||
=0
"Suppose there are n vectors, E1, E2, E3...En, and satisfy =0, then these n vectors form an orthogonal basis, that is, ||Ei||=1, now define Ai=, and get X= Ea, A= (A1, A2, A3...An), E= (E1, E2, E3...En)."

"Then the coordinates in the coordinate system are composed of these data, then..."

Fang Chao was still writing the data, but Shen Lang immediately understood Fang Chao's doubts, and immediately said, "Chaoer, why don't you try to use Fourier series?"

"Fuck!"

"Yeah, why didn't I think of using Fourier series? Brother Lang, you are simply a genius!"

The big man is indeed a big man!

Master Shen Lang knew where his confusion was before his problem was fully formed. This is not something ordinary people can do...

Where Fang Chao was somewhat blocked, such as a huge stone appeared on a road, Fang Chao was still hesitating whether to go around or find a way to move the stone away, because this stone was a coincidence. The place where it appears is very unusual, if the word is bypassed here, then it will appear in other places, like a lonely ghost, haunting you, always haunting you.

But when Shen Lang came out, he used the Fourier series. It is like a '卍' character, suppressing the dead ghost, making it unable to trap you forever. Now you only need to make a move, and you can beat it to death , even frustrated.

"Chao'er, let's imagine any function as a vector. Let's find a set of functions, such as sin(nx), cos(mx), then..."

Shen Lang himself randomly picked up a piece of draft paper from the ground, then took out a pen from his jacket pocket, and then wrote on the paper.

In the function interval 0~2π.

sin(nx)cos(mx)dx=0
cos(mx)cos(nx)dx=0，n≠m
sin(nx)sin(mx)dx=0, n≠m
"Chao'er, what did you think of?"

Fang Chao looked at the function written by Shen Lang, and at the same time connected with the Fourier series, he said without thinking, "Inner product."

The communication between Xueba is so simple, the two of them can understand what they say, Shen Lang just likes this, the only thing he loves in his life are two things, beautiful women and mathematics.

People don't need too many things to pursue in this life, just a little refinement is enough.

Shen Lang felt that he was okay, he only liked two things, and he could spend his whole life liking them.

As for beautiful women, he can talk freely with any beautiful woman about astronomy, geography, and even some slutty talk.

Only mathematics is sacred and cannot be explored and discussed in bed.

And now, he has found someone who can chat with him about mathematics. Although Fang Chao is still young, he is very malleable and talented. It won't take long for Fang Chao to catch up with him. Shen Lang felt a sense of pride in his heart when he thought of a rising star, and even made him thrive because of some of his own help.

"That's right, it's the inner product, then the above sin cos function becomes a set of orthogonal bases, and then take a closer look at the formula of the Fourier series, the Fourier series is nothing more than putting a function into this orthogonal Based on the projection. So the Fourier series is actually a set of "coordinates"."

"Of course, this coordinate is infinitely dimensional..."

(End of this chapter)