A4 paper sized paper is listed on three questions.

All three questions have traces of being drawn in circles.

Professor Lu naturally would not know in advance that Cheng Nuo would come to him to apply for no listening.

So……

The topics he seemed to have randomly drawn from the stack of materials on his desk were not specially prepared for Cheng Nuo.

Judging from the traces of the drawing on the paper, these three questions have been done once.

And that person is very likely Professor Lu sitting in front of him.

However, after figuring this out, it is of no use to Cheng Nuo's current situation.

No matter how these three questions came about and who had done them, Cheng Nuo wanted Professor Lu to sign the application form without listening, he had to do one of these three questions.

Choose one of three and do it right!

With Professor Lu's personality, being able to put forward such conditions is enough to prove that the three questions on the paper that Cheng Nuo was holding were definitely not ordinary people!

His power can definitely kill tens of thousands of poor students in an instant!

Cheng Nuo is not allowed to be treated uncautiously.

Cheng Nuo looked at Professor Lu at the seat sitting at the desk, walked up and said, "Teacher, I didn't bring my schoolbag here. Can you borrow a pen and draft paper?"

Professor Lu put down his pen, looked up at Cheng Nuo with a harmless smile on his face, bent down, opened the drawer of the desk, and handed the pen and draft paper to Cheng Nuo.

He pointed to a desk beside him, "You can do it there, call me after you finish it."

After saying that, he lowered his head again and continued the work at his hands.

Cheng Nuo was also obedient, took the pen and draft paper, walked to the desk that Professor Lu pointed to, pulled a chair and sat down.

The a4 paper with three questions was also spread flat on the table by Cheng Nuo.

Cheng Nuo looked at three questions in turn and decided which one to choose as a breakthrough point.

Question 1: [The elliptical cylinder surface is known.

r(u,v)={aosu,bsinu,v},-π≤u≤π,﹣∞≤v≤+∞

(1): Find the equation of any geodesic on s.

(2): Let a=b, take p=(a,0,0), q=r(u,v)={aosu0,bsinu0,v0}, -π≤u0≤π, ﹣∞≤v0≤+∞, write the shortest curve equation connecting two points p and q on s.]

Question 2: [Deduce the calculation format of the conjugate gradient method to solve the system of linear equations, and prove that the format converges after finite step iteration.]

Question 3: [Suppose f(x) is second order derivable on [0,1], and f(0)=f(1)=0,min(0≤x≤1)f(x)=-1.

Prove: There is η∈(0,1) so that f(η)》8.]

After reading these three questions from beginning to end, Cheng Nuo frowned.

The first question is a very comprehensive question.

Elliptic equations, trigonometric functions, differential equations, vector operations.

The combination of four aspects of contents has led to the extremely difficult problem of this question.

Solving the first question requires knowledge of vectors and trigonometric functions, which is not difficult for Cheng Nuo.

But the second question is mainly required to know about ordinary differential equations.

Regarding ordinary differential equations, it is actually involved in the last chapter of the first volume of the book "Advanced Mathematics" taught by Professor Lu.

However, it is originally a basic mathematics teaching book. What advanced mathematics talks about is just some of the most basic and simple solutions.

Maybe even the fur is not worthy of.

In the mathematics department, when I was in my sophomore year, there was a professional course called "Ordinary Differential Equations" that specifically explained this type of equation in detail. Cheng Nuo took the class with the mathematics department of this year's freshman year, so naturally he had not learned it yet.

Judging from Cheng Nuo's only knowledge at present, the second question should be to solve the problem using the Pika-Lindeloff theorem for solving ordinary differential equations.

But Cheng Nuo has only heard of Pika-Lindelof theorem. Cheng Nuo is still quite far from flexible application.

In the first question, Cheng Nuo can only give up strategically.

As for the second question, this made Cheng Nuo even more painful.

The so-called conjugate gradient method of system of linear equations is to obtain a large system of linear equations by differentially discrete laplae equations.

The requirement of the question is to perform continuous iterative operations on the general format of this system of equations, and determine the orthogonal system of equations through the recursive relationship of residuals, and determine the approaching convergence value.

If we talk about the solution method of differential equations in the first question, it is barely considered related to high numbers.

The second question, and what is explained in the advanced mathematics, is simply not related to the half-cent!

What are the conjugate gradient method, the laplae equation, and the residual recursive relationship, which is not what Cheng Nuo, a freshman, should master.

Indeed, like the previous question, Cheng Nuo has only heard of these contents.

As for solving the problem, sorry, Cheng Nuo really can't do it!

Originally, Cheng Nuo was thinking about solving all these three questions for him, which shocked Professor Lu.

But what about...the strength is insufficient.

However, it is fortunate that Cheng Nuo is very friendly to Cheng Nuo. As long as you use the special form of Taylor formula, the McLaurin expansion, and the relevant knowledge of Schlemirch-Rosh, you can perfectly solve it.

The Taylor formula is the most complex and difficult to understand in the first volume of advanced mathematics. It ruined countless geniuses here.

It is generally used for calculation errors. For general questions about Taylor's formulas, only simple formulas are needed to be substituted.

But the question in front of Cheng Nuo was not like this.

That really needs to be expanded one by one with the Taylor formula.

The workload is quite complicated!

But compared with those who can't do the first two questions at all, Cheng Nuo can only choose this question that tests the amount of calculation.

Start construction!

Cheng Nuo rubbed his hands and took a stack of draft paper in front of him.

Since you have selected the question, do your best to do it.

I must get it if I don’t listen to the application!

Close your eyes tightly, and your thoughts fly at high speed in your mind.

Half a minute later, Cheng Nuo's eyes suddenly opened and a flash of light flashed. The corners of his mouth were slightly raised, he picked up a pen, and wrote on the draft paper while calculating.

【f(x)=f(t)/0!+f'(t)/1!*(x-a)+f''(t)/2!*(x-a)^2…

…………

0=f(0)=-1+f''(t1)/2!x0^2

0=f(1)=…

Also because 0≤x≤1, f(η)=max{2/x^2,2/(1-x0)^2}≥8!】

Get it done!

After more than ten minutes, Cheng Nuo listed a whole sheet of a4 paper formula and finally calculated the question.

At that moment, I felt a sense of accomplishment.

After checking it and confirming that there was no problem, Cheng Nuo put on his pen cap, picked up his answer, got up and walked to Professor Lu.

"Professor, I'm done." Cheng Nuo spoke softly.

Professor Lu looked up at Cheng Nuo first, then raised his wrist to look at the time.

His slightly serious face also showed a slightly surprised expression.

Obviously, Cheng Nuo's speed exceeded his expectations.

He looked up and down seriously, but he was not in a hurry to answer the answer written by Cheng Nuo. Instead, he asked with a smile, "Which question are you doing?"

"The third way." Cheng Nuo answered honestly.

"Then do you know where I got these three questions?" Professor Lu said.

Cheng Nuo shook his head.

Professor Lu asked to say something, "Last year, the National College Student Mathematics Competition, the last three questions in the finals of the fourth grade finals are these three."
Chapter completed!