According to the syllabus of "Mathematical Analysis", it should first talk about the limits of the number series and the limits of functions, and then enter the field of Leibniz and Lopida, that is, derivatives and differentiation.

After Taylor and Riemann appeared, Taylor's formula and Riemann integral would run through the entire number of points, and even the entire career of mathematicians.

The above is the teaching content of Number I.

Normally, it looks like this.

It is clear that Professor Lu is not following the normal routine.

The calculation of double, triple, and n-fold integrals, as well as the concepts of the second type of surface integrals and the integration of the upper and outer differential forms of directional manifolds, are the teaching content of the second type of integral II.

All in all, Professor Lu did not copy the syllabus of the Ministry of Education, he had his own set of teaching plans, and Yan University was not under the control of the Ministry of Education, but the university was directly under the control of the central government.

In the past 30 years of research and teaching, Professor Lu has found a set of effective teaching system, he will not mess around, he is a full professor of Yan University, and he has won awards.

In Shen Qi's opinion, Professor Lu is at least at the level of mathematics level 8 or above, how can this kind of mathematical elite mess around?

Shen Qi likes Professor Lu's teaching style, yes, yes, between teachers and students, between classmates, there should be in-depth interaction, and the violent collision will inevitably produce an extraordinary reaction, and the exchange that goes straight to the soul brews the explosion of academic achievements.

Professor Lu introduced the topic to help students better understand the calculation methods, theoretical concepts and related skills of counting points.

In the first question, the two class leaders of the Department of Mathematics and the Department of Science and Engineering Computing showed their respective strengths, and Professor Lu expressed his approval.

Professor Lu continued his teaching style, and he came up with another problem, calculating the limit:

lim[x→0](e^x+e^2x+...... e^nx )1/x/n

"The first question was solved by the Department of Mathematics, supplemented by the Department of Science and Engineering Computing, providing new algorithms and ideas. Then the second question, please send a member of the Department of Science and Engineering Computing to the stage to find the limit. Professor Lu said.

"I'll come. Shao Tiantian raised his hand.

"It's you Shao Tiantian again, and the other students in the Department of Science and Engineering Computing don't have any ideas?" asked Professor Lu.

"No idea, no idea, he comes, he comes. Other students recommended Shao Tiantian to take the stage to win glory for the class and add color to the department.

"Okay, Shao Tiantian, Shao Tiantian, you come. "Professor Lu didn't have a choice.

Shao Tiantian came to the stage, brushed three times and divided five by two to complete the calculation, he looked at the audience with a smile, and he was in his chest.

"For Shao Tiantian's limit calculation, please comment on the students of the Department of Mathematics. Professor Lu looked at Shen Qi's position.

The Department of Mathematics was closely united around the center with Comrade Shen Qi as the core, and the people in their class were all sitting in a pile, except for Ou Ye and Zhou Yu'an in the back row.

"I'll start with that. Shen Qi nodded, "Shao Tiantian's calculation is completely correct, and my answer is the same as his." ”

"Oh. Professor Lu nodded, expecting Shen Qi to continue to analyze and comment.

Shen Qi: "I'm done. ”

Professor Lu: "Gone?"

Shen Qi explained: "The limit is such a thing, just calculate the answer, the process is routine, I believe that you can understand it when you look at it, and I won't be verbose." ”

"Don't even bother to give comments, and look down on our daily class leader?"

"In this way, then Shao Tiantian, you go down, your calculation is correct. Professor Lu respected Shen Qi's answer.

Shao Tiantian stepped down and laughed when he passed by Shen Qi's seat: "Hehe." ”

Shen Qi also smiled: "Hehehe." "One more than you, suppressing you in momentum.

The third question is the calculation limit, the double limit.

This time it was the turn of the Department of Mathematics to send a member, Shen Qi turned back to find Zhou Yu'an, and he conveyed a meaning to Zhou Yu'an with his eyes: Zhou Yu'an, you are on this problem, the limit is so simple, it is not appropriate for me to come forward to solve it.

Zhou Yu comprehended with peace of mind, and he came to the stage to solve this double limit problem.

According to the usual practice, Zhou Yu'an should analyze his own ideas before going down, fully share his successful experience with the majority of students in the Academy, and exchange and discuss together.

Zhou Yu'an and Shen Qi are in a dormitory, in his daily study and life, Zhou Yu'an also paid attention, he stole some mathematical skills from Shen Qi, and analyzed it like a river: "Dear students, do you know that it is much more difficult to find the double limit than the limit of the unary function, and the two are simply the difference between cloud and mud. ”

Because the domain of the unary function is the set of points on the real axis, the limit only needs to be considered from the left and right directions. ”

"The domain of the binary function is the set of points on the coordinate plane, in other words, the binary limit must take into account the approach route from any direction......"

Professor Lu was furious: "Zhou Yu'an, let's talk about the point! Everyone's time is precious, don't memorize textbooks for me here!"

"Okay, don't worry, Professor Lu, I'll get to the key part soon. Zhou Yu'an was neither panicked nor impatient, he continued unhurriedly: "Students, do you know that there are several ways to calculate the double limit? I am not good at learning, and I have only mastered five ways of calculation, the first is to use the definition to calculate the double limit, which is the simplest and most error-prone. ”

"The second is to use the trigonometric commutation method to calculate the double limit ......"

"Third, the continuity of the function is used to calculate the double limit ......"

"Fourth, I use the idea of the important limit of the unary function to find the double limit, and here I want to focus on explaining this fourth algorithm, which is also my core algorithm, which is used in the solution of the double limit problem of the blackboard. ”

"First of all, I want to explain that the idea of the important limit of a univariate function is used to find the double limit, and its core essence is ......"

Biu！

Professor Lu slapped his palm on the wall, and the blackboard shook: "Zhou Yu'an, I'll give you another 20 seconds! Obviously, the double limit algorithm that can be clearly explained in three sentences, you kid gave me a full five minutes! Zhou Yu'an, what are you?"

Hey, Shen Qi looked out the window speechlessly and sighed. Zhou Yu'an is too much to grind, originally he calculated this double limit is quite 6, this method I taught him, he showed well, I have won seven or eight points of true biography, at this time the most free way is to use a sentence to explain the core idea, and then coax down, it can be regarded as able to save some force.

But Zhou Yu'an is good, grinding and chirping like a girl, all the previous efforts are abandoned, brother, there is no force at all, and there is even a little LO, most women in this world are not as much as your Zhou Dazui's nonsense...... Shen Qi clenched his fists and cupped his cheeks, helplessly looking at the air outside the window.

At the same time, Ou Ye in the back row made a similar cheek support action as Shen Qi, hey, she also sighed, not knowing what her inner activities were.