Chapter 258: Differential equation, conjugate gradient, Taylor formula!

Three questions are listed on the a4 size paper.
The three questions are marked by circles.
Naturally, Professor Lu would not know in advance that Cheng Nuo would go to him to apply for exemption.
Then...
He seemed to pick out questions randomly from the pile of materials on the desk. It was not specially prepared for Cheng Nuo.
Judging from the traces of the circle on the paper, these three topics have been done once.
And that person is probably Professor Lu sitting in front of him.
However, having figured out this matter, it is of no use to Cheng Nuo's current situation.
No matter how these three questions came from and who had done them before, if Cheng Nuo wanted Professor Lu to sign the exemption application form, he had to make one of the three questions.
Choose one of three, do it right!
With Professor Lu’s character, being able to propose such a condition is enough to prove that the three questions on the piece of paper in Cheng Nuo's hand are definitely not waiting for you!
Its power can definitely kill tens of thousands of scumbags in an instant!
Cheng Nuo could not be treated with caution.
Cheng Nuo looked at Professor Lu sitting at the desk and walked forward and said, "Teacher, I didn't bring my schoolbag, can I borrow a pen and scratch paper?"
Professor Lu put down the 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 scratch paper to Cheng Nuo.
He pointed to a desk on the side, "Just do it over there, and call me when you are done."
After speaking, he lowered his head again and continued his work.
Cheng Nuo was 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 laid flat on the table by Cheng Nuo.
Cheng Nuo looked at the three questions in turn and decided which one to choose as a breakthrough.
The first question: [The elliptic cylinder s is known.
(u,v)=, -π≤u≤π, ﹣∞≤v≤＋∞
: Find the equation of any geodesic on s.
: Let a=b, take p= such that f(η)>8. 】
After reading these three questions from beginning to end, Cheng Nuo frowned.
The first question can be regarded as a very comprehensive question.
Elliptic equations, trigonometric functions, differential equations, vector operations.
The combination of the four aspects of content also led to the super-high difficulty of this topic.
Solving the first question requires knowledge of vectors and trigonometric functions, which is not difficult for Cheng Nuo.
But the second question, what is mainly needed is knowledge of ordinary differential equations.
Regarding ordinary differential equations, they are actually covered in the last chapter of the first volume of Advanced Mathematics that Professor Lu is teaching.
However, it was originally a basic mathematics teaching book, and the content of advanced mathematics is just some of the most basic and simple solutions.
Maybe even fur.
In the Department of Mathematics, there is a specialized course called "Ordinary Differential Equations" in the sophomore year that specifically explains this type of equation in detail. Cheng Nuo took classes with the mathematics department of this year's freshman year, and naturally he hasn't learned it yet.
From the current knowledge of Cheng Nuo, the second question should be solved by the Picard-Lindlov theorem for solving ordinary differential equations.
However, Cheng Nuo only slightly heard about the Picard-Lindlov theorem. With flexible use of distance, Cheng Nuo is still far away.
For the first question, Cheng Nuo can only give up strategically.
As for the second question, this made Cheng Nuodan even more painful.
The so-called conjugate gradient method of linear equations is to obtain a large-scale linear equations through differential discrete equations.
The requirement of the problem is to perform continuous iterative operations on the general format of this equation system, determine the orthogonal equation system through the recurrence relationship of the residuals, and determine the convergence value that is approaching.
To say that the method of solving differential equations in the first question is barely related to high numbers.
The second topic has nothing to do with the content explained in the high mathematics school!
Conjugate gradient methods, equations, and residual recurrence relations are not what Cheng Nuo, a freshman, should master.
And indeed, just like the previous topic, Cheng Nuo has only heard these contents.
As for solving the problem, sorry, Cheng Nuo can't do it!
Originally, Cheng Nuo thought that these three questions would be done for him, and he shocked Professor Lu.
But how... lack of strength.
However, Cheng Nuo is fortunate that the third question is very friendly to Cheng Nuo. As long as the special form of Taylor formula, McLaughlin's expansion, plus the knowledge of Schlemirch-Roche remainder, it can be solved perfectly.
Taylor's formula is considered the most complicated and difficult to understand in the entire high mathematics knowledge. Countless Tianjiao was ruined here.
It is generally used to calculate the error. For general questions about Taylor's formula, only simple formulas are needed.
But the question in front of Cheng Nuo is not like this~EbookFREE.me~ It really needs to be developed one by one using Taylor's formula.
The workload is quite complicated!
But compared with the first two questions, Cheng Nuo can only choose this question that tests the amount of calculation.
Let's start!
Cheng Nuo rubbed his hands and brought a stack of draft paper in front of him.
Now that you have chosen the topic, do your best.
That exemption application, I must get it!
He closed his eyes tightly, and his thoughts flew at high speed in his head.
After half a minute, Cheng Nuo's eyes suddenly opened, and a gleam of light flashed. The corners of his mouth were slightly tilted, he picked up the pen, and calculated while writing on the draft paper.
Get it done!
It took more than ten minutes for Cheng Nuo to list the formula on a whole piece of a4 paper, and finally figured out the problem.
At that moment, the sense of accomplishment was full.
After checking it again and confirming that there was no problem, Cheng Nuo closed his cap, picked up his answer, got up and walked to Professor Lu.
"Professor, I'm done." Cheng Nuo said softly.
Professor Lu raised his head and glanced at Cheng Nuo first, then raised his wrist to check the time.
His slightly serious face also showed a slightly surprised look.
Obviously, Cheng Nuo's speed exceeded his expectations.
He looked up and down seriously, instead of rushing to pick up the answers written by Promise, instead he smiled and asked, "What 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, please spit out a sentence, "Last year, the three questions at the final finals of the third and fourth grades of the National College Student Mathematics Competition were these three."
"At that time, no student was able to do all the last three questions correctly."