Shen Qi volunteered to come to the stage to solve the problem.

He has studied mathematics, counting I to counting III, and he has studied it before he came to Yan University.

Not to mention the basic courses of the freshman year of mathematics, such as number fractions, high algebra, and solutions, Shen Qi also completed the follow-up professional courses such as complex variable functions, partial differential equations, and topology.

College is not a high school, the sky is high here, the birds fly, those who can work hard, and if you have the ability and energy, then learn more, no one will let you learn.

Put Shen Qi and a few other students with outstanding skills in the big classroom, and receive basic education with other students, the professors may have their own arrangements, Sun Erxiong told Shen Qi, at least in the freshman year, Shen Qi You have to come to the big class to listen to the lectures.

Professor Lu's math question written on the blackboard is a bit excessive, he is embarrassed for the freshman, this question has gone beyond the scope of basic education, and today's math lesson is Professor Lu's second class.

In universities, especially in the highest institutions such as Yan University and Mizuki, it is not enough to rely on the dozens or hundreds of class hours in the classroom.

"It's not easy to use a one-piece projection for this question, so you have to use a faceted projection. Shen Qi sorted out his thoughts again and wrote his answer on the blackboard.

The equation for S is x^2+y^2=4, which is not a continuous function like z=z(x,y), and it is difficult to find the normal vector of the side where S is located.

If the faceted projection is used, the projection of the cylindrical surface in the XOY plane is a line, which is actually a circle, so ∫∫(z+l)dxdy=0

Next, Shen Qi began to calculate the value of ∫∫-ydzdx.

To determine the range of values of x and z, it is necessary to make a plot, Shen Qi made a plane projection diagram on the blackboard, and finally calculated I=-8π.

Shen Qi put the chalk back into the slot, patted the chalk ash on his hand, and said to Professor Lu, "The solution is complete." ”

Professor Lu: "Shen Qi, you have given an answer, I will not judge your answer for the time being, please tell us your thoughts." ”

"Good. Shen Qi stayed on the podium, and his position was the professor's seat.

Professor Lu stood on one side, holding his hands in his hands.

Knock knock.

Shen Qi knocked on the blackboard: "y is the cylindrical surface x square plus y square is equal to 4 about the odd function of plane XOZ symmetry, the 'S front' I write here refers to the cylindrical surface x square plus y square is equal to 4 in the part where y is greater than 0, so y is equal to 4 minus x squared and then squared." You can understand what I'm talking about, right?"

"Well, that makes sense. Zhou Yu'an nodded.

"That's what I thought, too. Roji agreed.

"Shen Qi's thinking is OK. Cai Qing wrote and drew in the notebook.

Ou Ye didn't speak, the result she calculated was exactly the same as Shen Qi's, and the calculation method was different.

These people were on the same channel as Shen Qi, and while Shen Qi was answering on the blackboard, they also came up with the answer in their own way.

The other students in the Department of Mathematics were half a beat slower, but after Shen Qi wrote out his solution process, they could roughly understand that after all, more than half of the students in the Department of Mathematics were sent to Yan University through mathematics competitions, and they had a solid foundation in mathematics.

From last autumn to this autumn, Shen Qi was not the only one who enriched himself in a year.

Every student in the Mathematics Golden Autumn Camp, Sun Erxiong gave directional suggestions.

You can learn a lot of knowledge on your own in a year, and if you really settle down to learn.

"Shen Qi, pause. Professor Lu interrupted Shen Qi's analysis of his train of thought and pointed out the student's name: "Zhou Yu'an, you come to analyze and analyze, is Shen Qi right? ”

Zhou Yu'an replied with certainty: "Shen Qi, what he said is very right." ”

"Don't be so general, details, I need details. Professor Lu looked at Zhou Yu'an.

Zhou Yu'an talked eloquently: "In fact, Shen Qi's previous derivation calculations are all conventional routines, the picture he drew is the highlight, the second type of three-dimensional picture of the surface division is very troublesome to draw, Shen Qi simplified the complex, drew a projection of a certain plane, determined the value range of x and z, and finally calculated that I is equal to -8π." I gave Shen Qi 99 points for this wave of operations, and I didn't give one point left, because I didn't know whether Shen Qi's answer was correct or not, and I needed Professor Lu to judge. ”

Professor Lu asked Shen Qi instead: "Shen Qi, what do you want to say about Zhou Yu'an's comments?"

Shen Qi propped his hands on the stage of the podium and looked at Zhou Yu'an: "Zhou Yu'an, regarding your comments on me, I will give you 99 points for this wave of operations, and I won't give you any points left, because you talk too much nonsense." ”

"Cut. Zhou Yu'an smiled and made a gesture of "I don't accept you to hit me".

The atmosphere of the subject is quite lively, Professor Lu deliberately created this atmosphere, and even the mathematics professors admit that mathematics is a boring course, and if a boring course is explained in a dull way, how many students will really like this course?

Shen Qi's answer, as well as Zhou Yu'an's comments, are no problem. The answer given by Shen Qi is correct, yes, it is -8π. Professor Lu said, and said to Shen Qi: "Shen Qi, you can return to your place, please return my podium to me." ”

Shen Qi stepped off the podium and returned to his seat.

Professor Lu returned to his position, returned to the center of the podium, and knocked, he picked up the blackboard and knocked on the blackboard, and the position of the knock was the plane projection diagram drawn by Shen Qi: "Here is the key point, you have to remember it." ”

The students from the mathematics department in the audience took their pens and notebooks, ready to memorize the key points.

Most of the students in the Department of Science and Engineering Computing are at a loss, the focus, what is the focus, where is the focus, why is the focus, why is there a focus all of a sudden? Ah, where am I, who am I, where am I going......

There is no harm without contrast.

The overall foundation of the students in the Department of Mathematics is one street stronger than that of the Department of Science and Engineering Computing.

In fact, counting is a very important course in the Department of Science and Engineering Computing, and counting is almost a purely applied course, it is a mathematical calculation tool. It may be that the school has just started, and the students of the Department of Science and Engineering Computing have not yet entered the state.

Professor Lu came up with a question, asked students to answer, let students talk about ideas, and then asked other students to make comments.

Let students teach students, so why do you need to teach?

The professor is of course the one who puts the finishing touch, and Professor Lu concludes: "I have already said in the last lesson, and now I will emphasize again the symmetry of the second type of surface integral, which is exactly the opposite of the law of the odd functions of double and triple integrals. You can understand it, right?"

"If you don't know too much, students should spend more time thinking about it after class, most of you have received early education such as the Golden Autumn Camp and Winter Camp of Yan University, don't tell me that you have only started to get in touch with mathematics in the past few days. ”

The students who had not participated in the training camp of Yan University asked Cangtian speechlessly, their number was not large, and a small number of them were admitted to the Yan University School of Mathematics through the college entrance examination.

This small group of students is divided into two situations, one is that they consciously and voluntarily fill in the mathematics major of Yan University when filling in the volunteers, and the other is that they have a high score in the college entrance examination, and the first choice is to fill in Yan University but did not choose the mathematics major, and they don't know why they came to the Yan University Mathematics Institute in a daze. In both cases, half and half.

Professors sometimes have to make a choice, do they care for the majority, or do they care for the minority?

Professor Lu's approach is to take care of the majority.

Therefore, those students who don't understand too well can only redouble their efforts to catch up, otherwise they will fall behind, and the more they go behind, the more they will not be able to keep up with the progress of the large army.