Chapter 174

The next day, Friday.

After finishing the freshman mathematical analysis class in the first two periods in the morning, Gu Lu did not go back to the office, but came to classroom 402 upstairs according to the class location provided by Teacher Shi.

Gu Lu came to the classroom five minutes early.

After a glance, I saw that almost all the students in the classroom had arrived.

The third year of mathematics and application majors, like the first year, has only one class, about forty or fifty students.

But here's the difference.

In the first-year mathematics class, there is at least a female classmate like Bai Yao who supports the façade of the girls in the mathematics department.

The third-year mathematics department is all a man.

Females or something, completely non-existent!

When Gu Lu first walked into the classroom, the students didn't notice Gu Lu at first.

Instead, they stared at the real function textbook in front of them one by one, looking bitter and hateful, and frowning.

From their expressions, Gu Lu read the words "There is no love in life".

Indeed, all beings are equal in the face of the real function.

Even the top students of the Department of Mathematics of Yan University are no exception.

The class bell rings.

"Ahem. ”

Gu Lu coughed lightly, shifting the students' attention from the textbook to himself.

The classmates raised their heads, their eyes fell on Gu Lu, and then their eyes became confused.

Who is this buddy?

Many students wondered.

Gu Lu smiled slightly, propped up the lectern with both hands, and looked at everyone in the audience, "Presumably the teacher has already told you." He couldn't come to this class, so he found someone to come over and substitute for him. And I'm your substitute teacher. ”

"Uh...... I would like to ask. A boy sitting in the first row raised his hand and asked, "Are you a senior, or are you ...... Teacher?"

Gu Lu's age really doesn't look like the math teacher they remember.

If it is a senior who is studying for a doctorate, many of them believe it.

It's just that this hair is kept too intact, and I must ask this senior after class what secrets he has to prevent hair loss.

Learning their math and having thick black hair is not just the dream of many people.

Gu Lu kept a smile and answered the boy's question, "I am a 2012 mathematics student, you can call me senior." ”

"But more formally, I'm a lecturer at the Yan University School of Mathematics, do you need me to show you my teaching certificate?"

The male classmate smiled and waved his hand, "No, no." ”

Gu Lu shrugged, picked up a piece of chalk, and looked at the forty-odd people in the audience with a smile, "If there is no doubt, then we will start today's lecture." ”

"In the last class, your teacher finished talking about the integral part of the measurable function, and in this class, we will talk about the next chapter, which is the core content of the whole course of real variable functions - Lebesgue integral!"

The Lebesgue integral, known as the Lebesgue integral in Chinese, is the core of the real function, which extends the integration operation to any measure space.

Again, as a core course in the course of real variable functions, it is understandably more difficult to understand.

Some of the foreshadowing content, such as some knowledge of measures and measurable functions, has already made many students big.

As for the core Lebesgue points, the difficulty of learning can be imagined.

Many students are already scared before they even learn.

Just before class, the students stared at the textbook one by one, not for other reasons, but because they were previewing the content of Lebesgue points.

But......

I don't understand it at all!

real functions, and advanced mathematics.

Although both courses talk about integrals, the difficulty of the course is completely one heaven and one underground.

Taylor's formula, which is the most difficult in advanced mathematics, is a simple thing that can no longer be simple in front of students who study real functions.

In the face of real functions, advanced mathematics is a younger brother!

Not only advanced mathematics, but also linear algebra, complex functions, and number theory, all of which are younger brothers!

The students in the first class of junior mathematics are now desperate in their hearts.

Originally, the content of Lebesgue points was outrageous.

If you want to be able to understand it on your own, only a very small number of people can do it.

Most of them need to be explained by the instructor.

However, coincidentally, when it came to this part, their teacher happened to have something to do.

Then ask a young teacher who can be their senior to come over and help with the substitute teaching.

This is...... Heaven will kill me!

The students all had empty eyes and gray eyes.

I just hope that this new teacher doesn't give a bad lecture!

The students don't expect too much, they just ask Gu Lu not to talk too badly.

…………

on the podium.

A smile appeared on the corner of Gu Lu's mouth.

"Consolidation function?" Gu Lu muttered softly.

To tell the truth, when Gu Lu was studying this real function course in college, due to the influence of rumors, Gu Lu was on guard against this course.

However, after learning it, Gu Lu began to doubt the authenticity of the rumors.

Solid function, but that's it!

Is it difficult?

But I don't feel it at all.

In two months, Gu Lu listened to the lectures and studied on his own, and easily mastered the content of this course, and then began to take another course.

Therefore, the difficulty of the real function only varies from person to person.

The rumored feeling of being tortured to death, Gu Lu unfortunately did not experience it.

As for the understanding of the course on real variable functions......

Gu Lu has a doctoral degree, and no matter how difficult the real variable function is, it is only an undergraduate course.

In Gu Lu's theory, the difficulty of all undergraduate courses is the same.

Because they are all the lowest, foundational courses.

And Gu Lu is now, according to the way he learned the real function at the beginning, and explained the key content of Lebesgue integration to the students in the audience.

…………

Gu Lu turned around, wrote down a formula on the blackboard: S=∫(a,b)f(x)dx.

This is the Riemann Points.

Although Mr. Shi gave Gu Lu a PPT for teaching, Gu Lu never had the habit of speaking PPT.

As a math teacher, he still prefers the feeling of using chalk and writing down formulas on the blackboard.

And there is another reason, that is, the explanation ideas given by Mr. Shi on the PPT are a little different from Gu Lu's lecture ideas.

So he wrote directly on the blackboard.

Gu Lu knocked on the formula on the blackboard and asked the students below, "What is this formula?"

"Riemann points!" replied neatly.

Gu Lu smiled and nodded, "The Riemann integral is an accurate definition of the integral of a function on a given interval. However, there are certain drawbacks to the Riemann integral. So, the Lebesgue points appeared!"

Below, I will take the Riemann integral as a starting point to introduce the emergence and development of the Lebesgue integral. ”

…………