Become a master from now on

Chapter 259 Maybe Qingbei is really a good choice (please subscribe monthly pass!)
Fang Chao accepted the 10000 yuan transferred from Fang Yuanyang, and at the same time praised his father.

After eating, I feel sleepy.

Feel full and warm.

He stayed up all night for seven days and seven nights, and basically slept for no more than three hours at night. Whenever he had an idea, Fang Chao got up to work. The light in his room was almost turned on every night and during the day, unless When I'm particularly tired, I just go to bed and lie down for a while.

But most of the time, he just slept on his stomach on the table in his room.

Now that the waveguide function has come to an end, the rest is left to Shen Lang, and he has nothing to do. At this time, he can feel his upper and lower eyelids fighting, and no one accepts the other. In the end, he did it directly. It is inextricable...

This sleep was so dark, the sun and the moon were dark, and Fang Chao didn't wake up for a whole day and night. Fang Chao woke up at around four o'clock in the afternoon the next day. He was disturbed by the ringing of his mobile phone. Awake.

He is still a student, not many people know his mobile phone number, and it is still class time, basically it will not be someone from the school looking for him.

Shen Lang!

The note on the caller ID is Shen Lang.

Got news?

Fang Chao woke up all of a sudden, no longer feeling sleepy.

He puts the phone through.

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

Shen Lang quickly said, "I took a brief look at your waveguide function. The problem is not big. I didn't expect that you could come up with such a function equation at the age of 17."

Fang Chao said, "I also had a whim."

Shen Lang said again, "About the function equation you uploaded to me this time, I read it, whether it is an example or a train of thought, etc., there is no big problem. I only have a few questions for you personally."

Hearing what Shen Lang said, Fang Chao breathed a sigh of relief.

There is only one reason why Shen Lang said this, and that is that the waveguide function he calculated was established. This is a brand-new idea. Although it is not as great as Kaijiang, it can provide high school students with an insight into the calculation method of function solutions. Better ideas.

The seven consecutive days of fighting were not in vain, and Fang Chao was definitely filled with excitement!

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

Shen Lang: "First of all, the first point is the domain of f(x). I haven't seen it in the materials you sent me. If it's not because I know what you want to express, I will focus on this question. , your waveguide function is not valid."

When Fang Chao heard this, he slapped his forehead directly, "Dizzy, I forgot about this..."

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

Shen Lang said it was just a small problem, it was from his side, because he is also a genius, and it is not too difficult to understand the genius' thinking, but what about the others?
A wise man has a thousand worries, and he must have a loss!
Fang Chao said helplessly, "I didn't expect that I made such a huge mistake in this aspect. It really shouldn't be. I should reflect on it."

Shen Lang said, "It's not a big problem, don't be nervous, it's just some routine problems and mistakes, which can be avoided."

Fang Chao, "Yeah."

Shen Lang, "Within the domain interval you mentioned, how to determine the sign of f(x) at the endpoint?"

Fang Chao continued to answer, "If the sign is different, then f(x) has only one zero point in the interval, if the sign 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 of f(x)."

Shen Lang: "Alright, so what do you think about the approximate value?"

Fang Chao: "Approximate calculations using derivatives, the main idea is to use tangents instead of curves when x is sufficiently close to x0."

Shen Lang, "Well, how do you calculate it?"

Fang Chao: "When |x| is very small, an approximate equation is obtained, △y=f(xo+△x)-f(xo)≈f'(xo)△x, f(xo+△x)≈f(xo) +f'(xo)△x, let x=xo+△x, f(x)≈f(xo)+f'(xo)(x-xo)

In particular, when xo=o, |x| is very small, f(x)=f(o)+f'(o)x..."

The topic was Fang Chao's idea, and the entire problem-solving idea was also solved by Fang Chao. Fang Chao answered all the questions raised by Shen Lang fluently without any 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 said with a smile, "The questions are just the ones I just asked. It's not a big question. I just need to provide additional explanations, because there are many things you have to answer." To write it down, mathematics is like this. Even if you know it, the process and definition of the calculation are also very important."

Fang Chao said, "Thank you Brother Lang."

Shen Lang, "It's not a big deal, it's just how you think about what I said? Do you want to come to Qingbei? If you come to Qingbei, there will be absolutely no problems in mathematics. Besides, even if you want to go to Princeton in the future, you will never have any problems. It’s not a bad idea to start from Qingbei. Could it be that Qingbei is really inferior to Peking University? It’s not that unreasonable. Besides, if you come to Qingbei, Professor Lin will also provide you with convenience. In the future, I will write a recommendation letter to Princeton. You are a student at Princeton."

Shen Lang is still thinking of a way to drag Fang Chao to Qingbei, so that the two swords of the brothers and sisters will be invincible in the world.

After hearing this, Fang Chao felt a little moved in his heart. He wanted to go to Peking University before. That was because the road from Peking University to Princeton was a shortcut. Besides, there were indeed many seniors from Peking University in Princeton, so Fang Chao wanted to go to Princeton through Peking University.

But because of this, he also fell into a misunderstanding, that is, if he wants to go to Princeton, is there really only one way to go to Peking University?No, Qingbei is also fine!

Besides, is Princeton recruiting students because of your Peking University's face?

Obviously not!

As long as you have the ability, you can pass the admissions of Princeton anywhere.

You need to be hardworking yourself, not to mention that Fang Chao's own level has no problems, so what's the difference between going to Peking University or Qingbei?

Fang Chao said, "Brother Lang, I will seriously think about what you said, maybe Qingbei is indeed a good choice."

(End of this chapter)