Fang accepted the 1oooo yuan transferred from Fang Yuanyang, and also praised his father for his performance.

After eating, I was sleepy.

Think about it with warmth.

He kept nights for seven days and seven nights, and his sleep time was basically only three hours at night. Whenever he had an idea, he got up to do his homework. The lights in his room were almost off. They were on every night and also on during the day. He would only lie in bed for a while when he was very tired.

But for more time, he just slept on his desk in his room.

Now the waveguide function has come to an end, and the rest is left to Shen Lang, and he has nothing to do. At this time, he feels that his upper and lower eyelids are fighting, and no one is convinced. In the end, he just started to do it, and it is difficult to solve...

This sleep was so dark that the sky was dark, the sun and the moon were gone, and I didn't wake up for a whole day and night. I woke up at around 4 o'clock the next afternoon. He was awakened by the ringtone of his cell phone.

He is still a student, and not many people know his mobile phone number, and now it is still time for class, so basically no one from the school is looking for him.

Shen Lang!

The notes for the caller ID are Shen Lang.

Any news?

Fang suddenly woke up and was no longer sleepy.

He answered the phone.

"Brother Lang, how about it? Is there any problem with the waveguide function equation I wrote? Is there anything that needs to be corrected?"

Shen Lang quickly said, "I took a rough look at your waveguide function. The problem is not very big. I didn't expect that you could come up with such a function equation when you were only seventeen years old."

Fang said, "I also had a sudden idea."

Shen Lang said again, "I have read the function equations you uploaded to me this time. There are no big questions, whether it is examples or ideas, etc. I personally only have a few questions to ask you briefly."

Fang was relieved when he heard Shen Lang say this.

There is only one reason Shen Lang said this, that is, the waveguide function he calculated is valid. This is a brand new idea. Although it is not as great as Kaijiang, it can provide high school students with a better idea about the operation methods of function solutions.

The seven consecutive days of hard work were not in vain, and Fang was absolutely surging in his heart!

"Brother Lang, please ask if you have any questions."

Shen Lang: "The first point is that the domain problem of f(x). I have not seen it in the materials you gave me. If it weren't for the fact that I knew what you wanted to express, just focus on this question, your waveguide function would not be valid."

Fang heard this and slapped his forehead, "Damn, I forgot this..."

When he was thinking about this question, he naturally had a domain in his mind, but he did not express this domain because he knew it, but if he knew it, it did not mean that others knew it too. This is a huge problem and it is very serious.

Shen Lang said it was just a small problem, that was from his side, because he was also a genius, and it was not too difficult to understand the genius’ ideas, but what about the others?

A wise man will make a mistake if he has a thousand thoughts!

Fang said helplessly, "I didn't expect that I had such a huge mistake in this regard. It's really not necessary. I should have to reflect on it."

Shen Lang said, "There is no big problem, don't be nervous, it's just some routine problems and mistakes that can be avoided."

Fang, “Yeah.”

Shen Lang, "How to judge the symbol of f(x) at the endpoint within the definition range you mentioned?"

Fang continued to answer, "If the number is different, then f(x) has only one zero point in the interval. If the number is the same, then f(x) has no zero point in the interval. If the value of f(x) at a certain endpoint is zero, then the endpoint is a zero point in f(x)."

Shen Lang: "Okay, then what do you think about the approximation?"

Fang: "When applying derivatives to perform approximate calculations, the main idea is to use tangents instead of curves when x is fully close to xo."

Shen Lang, "Well, then how to calculate it?"

Fang: "When｜x｜are very small, get the approximate equation, yf(xox)-f(xo)f'(xo)x,f(xox)f(xo)f'(xo)x, let xxox,f(x)f(xo)f'(xo)x

Especially, when xoo,｜x｜are very small, f(x)f(o)f’(o)x…”

The question is what Fang thought, and the entire problem-solving idea was also solved. Fang answered all the questions raised by Shen Lang and had no questions.

He can be said to be familiar with every step.

The two chatted on the phone for more than an hour, and then Shen Lang smiled and said, "The questions are just the ones, they are not considered big problems. They just need to be explained additionally, because you have to write many things out. This is how mathematics is. Even if you know, the verification process and definition are very important."

Fang said, "Thank you, Brother Lang."

Shen Lang, "It's not a big deal, just what I'm talking about? Do you want to come to Tsinghua University? If you come to Tsinghua University, there is absolutely no problem with mathematics. Besides, even if you want to go to Princeton in the future, it's okay to leave from Tsinghua University. Could it be that my Tsinghua University is really worse than Peking University? I don't care. Moreover, if you come to Tsinghua University, Professor Lin will provide you with convenience. In the future, you will write a letter of recommendation to Princeton, and you will be a student of Princeton."

Shen Lang was still thinking of a way to pull Fang to Tsinghua University, so that his brothers and brothers could combine their swords and be invincible in the world.

Fang heard that he was a little moved. He wanted to go to Peking University before, because the road from Peking University to Princeton was a shortcut. Moreover, there were indeed many seniors from Peking University in Princeton, so he thought about going to Princeton through Peking University.

But he also fell into a misunderstanding, that is, if he wants to go to Princeton, is it really the only way to Peking University? No, Tsinghua and Peking University are OK!

Besides, is it up to Princeton to recruit students based on your face?

Obviously not!

As long as you have the ability, you can recruit students anywhere you are.

To make a blacksmith must be strong, not to mention that there is no problem with Fang’s own level. So what’s the difference between going to Peking University or Tsinghua University?

Fang said, "Brother Lang, I will think about what you say seriously. Maybe Tsinghua and Peking University are indeed a good choice."
Chapter completed!