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Chapter 162 Advanced Mathematics Lecture 1

Tuesday, April 1, 1203, Qiyao Calendar.

The main building of Thorz Military Academy has three floors. Entering from the main entrance, on the left hand side are the fixed classrooms for military cadets. Second-year Classes I~V are on the first floor, and First-year Classes I~V are on the second floor. Some small classrooms

Courses for class and grade-level instructors will be completed in the class classroom. The first floor on the right is the faculty office, and the second floor is the classroom for various professional courses. Including music classroom, cooking classroom, art classroom, and guidance terminal room.

and a lecture theater specifically used for large courses.

The so-called large course is a type where multiple classes take classes together. Dean Van Dyke’s Military Science, Dean Henry’s Political and Economic Ethics, Ling’s Advanced Mathematics, and Makarov’s Natural Science all share the same lecture theater.

Each row of the lecture theater is divided into 5 seats on the left, center and right. There are 8 rows of seats in total and can accommodate up to 120 students. That is, all students of a single grade can attend classes together. However, only classes hosted by the dean in person will allow aristocratic classes and civilians to attend classes.

The classes are held together, and the major classes given by the other instructors are held separately for the aristocratic class and the civilian class.

Pointers and chalk are very familiar teaching aids to Ling.

Since resigning from Luray University of Technology in June 1201, Ling went to major universities to hold open classes until September, and then took a long vacation for herself. Almost a year and a half has passed.

Now that I am back in education, I feel a little nostalgic.

In the past, Thorz's mathematics instructors would spend half a semester consolidating the foundation of Sunday school, giving students with insufficient academic ability a period of adaptation before starting to study matrix algebra and differential equations. But Ling's side was a little different.

The subject she is responsible for is advanced mathematics. Strictly speaking, it is not the same thing as the (elementary) mathematics learned in Sunday school. This was newly developed when she was a professor of mathematics, physics and chemistry at Luray Institute of Technology.

The course is divided into four parts: pure mathematics, mechanical mathematics, statistical mathematics, and decision-making mathematics. It sounds like there are some overlaps with the natural science courses of Instructor Makarov, but in fact the difference is quite big.

Instructor Makarov's courses tend to focus on theoretical applications, which are explanations and explanations of natural phenomena. Most of them are text-based. If your understanding is strong enough, then this course will go smoothly. Ling's course is about calculations.

, a lot of calculations. It not only requires understanding of concepts, but also exercises everyone's calculation ability. Even if 80% of the original lesson plan is deleted according to Makarov's suggestion, the remaining part is enough for Thorz's new students.

Let's drink from a pot.

"Instructor Ling, good morning!"

The first person to come to the lecture theater was Tova. There is a morning exercise system in the Military Academy, and the drills are usually led by grade-level instructors. However, there is still a long break between the end of the morning exercise and the first class.

Towa came over early to regain her strength and energy. It seemed that the military training in the morning did not put any burden on her.

"Well, good morning. Since you're here, can you help me distribute the handouts? You can also preview today's content. For you who ranked first in the entrance test, today's course should not be burdensome."

"Okay. The first period is instructor Ling's class. It feels great."

Even if the course is difficult, it won't be a burden to a top student like Towa.

"By the way, you will be the class representative. I'll leave it to you if I stand up."

There are 16 people in the first class and 16 people in the second class. A total of 32 people.

The third class has 18 people, the fourth class has 15 people, and the fifth class has 15 people. The total number of civilian classes this term is 48 people.

With Ling's memory, it only takes a few minutes to memorize all the new students' information, but her impression of the students is only a superficial understanding of their names, genders and birthplaces. This is only the information that needs to be used when taking roll call in each class.

.There is a decisive difference between higher education and previous education. Lecturers only complete the planned coursework according to the curriculum and will not care about other things.

The same was true when Ling was a professor at the University of Technology. As a professor, she only lectured but did not care whether the students listened or not. Even if the students were using portable guidance terminals to play bombs, as long as it did not affect other students'

She will ignore it if she learns.

We are no longer children. We have the right to study or not to study, the right to choose not to pass the exam, and the right not to graduate. Of course, we also have the right to choose not to accept the knowledge taught by the teacher.

If you fail the exam, you will retake it. If you fail the retake exam, you will retake it. If you fail the retake exam, you will not graduate.

According to the school rules of the strictly disciplined Thorz Military Academy, it is possible to be expelled directly once you have failed more than ten subjects. However, this school rule has not been implemented in the past 100 years. Although there are voluntary dropouts

students, but almost no students were expelled by the dean. Those who can get into Thors, whether they are in the aristocratic class or the civilian class, are very outstanding talents, and there are almost no people who deliberately commit stupidity.

In the first class, it wasn’t like anyone was absent from class. Even Crow came to class.

Before the class bell rang, all the students were seated. Ling designated Tova as the class representative, responsible for assisting her in signing in before class, distributing handouts, collecting homework and other chores.

"Standing up ceremony"

After Towa shouted late, all the students stood up quickly and shouted "Hello, instructor" to Ling in a loud voice. The scene was really amazing, and it is not an exaggeration to say it was pleasing to the eye. It should be said that they are worthy of being military academy students, ordinary students

The school cannot be so tidy.

"Sit down"

The Institute of Technology is not so rigid, but this is the tradition of the Military Academy, and Ling has no intention of changing it.

"Dear classmates, I am very happy to have the opportunity to teach you mathematics for one academic year. I also taught mathematics for two years from 1199 to 1201 at the Luray Polytechnic University in the Black and Silver Steel City. The Torz Military Academy serves as the Erepo

Although the entrance threshold for the super-first-class universities in the Nian Empire is not as good as that of the Metropolitan Academy, the Imperial Academy of Sciences, and the Xion Business School, as a traditional prestigious school with a long history, the admission score of Thors is far higher than the background.

Luray University of Technology, which is famous for research and development, is much higher. I guess your grades will be much better than students at Luray University of Technology, so you should be careful. I am going to write a report after I finish teaching.

, discussing the comparison between the students of Luray University of Technology and the students of Thors Military Academy. So you can also say that you have to bear a little responsibility for Thors’ reputation.”

Ling looked around and saw that many students were frightened by her statement, and she was quite satisfied with the effect of her intimidation. Although there were also students like George who were originally studying at the Polytechnic University among the students here, most of the students in the civilian class were

She received a Sunday school education and took the Unified Graduation Examination when she graduated, and was admitted to Torz based on her strength. And Tova's grades were even so good that she won first place in the entire Imperial Capital school district. Generally speaking, this kind of top talent is in

In previous years, those who would have been snatched away by the Imperial Academy. (The Empire has the "College Entrance Examination". This second setting is based on the meal at Tova's house in Flash 3. It was learned from Martha Herschel that Tova came to Thors for a scholarship.

(without going to the academy)

"You don't have to be so restrained. I graduated from Thors in 1199, so I can be regarded as a senior who is six years older than you. Some of you may have heard of my name, but most of you

You probably don’t know much about it. Before the course officially starts, let me introduce myself first. My name is Ling Astre. I was born in the state of Chasarante in 1185. Yes, you heard me right. I am the oldest of all of you here.

Some of them are students of the same year. Don’t be surprised. The empire is so big. Occasionally there will be students like me who did not take the unified graduation examination, but were confident in their academic ability and passed the self-study exam in advance to enroll in Thors."

Including Angelica, George, and Tova, most of the 220th class of Thors were born in 1185. Even Crowe, who was actually one year older, forged his identity of being born in 1185.

The regulations of the Imperial Army's regular army stipulate that you must be of age to serve as an officer (although this provision is not strictly enforced in fact, and there are many underage officers in the Imperial Army). Thorz is a two-year system, so in this way

You can reach adulthood in the year you graduate at the age of 20. If you want to become a professional soldier and join the Imperial Army, you can start directly from the officer class. The remaining few were born in 1186, that is, they graduated from Sunday school at the age of 16.

After graduation, they entered Thors directly. Few of these people signed an agreement with the Military Academy. Most of them did not regard Thors as a military subject, but as an ordinary university.

Torz has very special regulations. In addition to top students like Tova, whose test scores far exceed the admission limit, can enjoy generous scholarships, there is another way to waive tuition and obtain scholarships, and that is to contact the university before enrolling.

The Military Academy signed an agreement and promised students to join the Imperial Army after graduation. This group of students accounts for about a quarter of civilians, both boys and girls. From what Ling knows, the 220th class of middle school students

The people who fall into this situation are one person in Class 3, three people in Class 4, and eight people in Class 5. Different from the military students who have not signed a contract, they have joined the military from the day they officially start class. They will obtain military status when they join the school and join the army.

During the period of studying at the school, military service was calculated. In addition to Thorz's scholarship, there was also military pay from the Imperial Army. Although the Mira received was not much, it was only equivalent to the minimum allowance of a private soldier.

After Ling introduced herself, the doubtful glances of the students were reduced a lot. The reason why Ling and everyone were peers was so easily accepted because of the existence of Towa in the class. If there was only one of them, they might still care.

, but since there are two little guys, it doesn’t seem so strange.

"Okay, let's get started. Mathematics, everyone starts learning it when they enter the first grade of Sunday school. Mathematics is the oldest subject. It has been closely related to mathematics since human civilization. What the students learned in Sunday school

Most of the mathematical knowledge in mathematics comes from before the Great Collapse. In the era when the power of the treasure given to mankind by the goddess Edes has not yet disappeared, people living in affluence have greatly developed mathematics in order to pursue the mysteries of the world. Thanks to Qiyao

The church’s efforts over the past thousand years have well preserved the results of research at that time. Elementary geometry and elementary algebra are what everyone learned in Sunday school. Simply put, the characteristics of mathematics have two aspects. One is aesthetically speaking.

, it is unparalleled beauty!”

It was not because of the influence of Blubrand that he suddenly said such a sentence. Ling was teaching very seriously.

"Mathematics has its own aesthetic value, which is different from the beauty shown in poetry, drama, sculpture, music, and painting. It is an abstract beauty, a cold beauty, and a precise beauty. This is its

The first characteristic. Another characteristic is that it is useful. Its practicality is reflected everywhere in our daily life. Measuring land, living expenses, calculating cashiers, counting populations, firing cannonballs... it is used almost everywhere in life.

Mathematics. All students have done application problems, which are mathematical problems that are combined with reality. In order to avoid ambiguity, I have abstracted the mathematics that only leaves numbers into pure number mathematics, and the applied part is divided into mechanical mathematics.

There are three major categories: statistical mathematics and probability mathematics. Although there are some branches of mathematical applications that cannot be covered by the above three major categories, they are not the discussion content of our courses and will not appear in the exam. If you are interested in learning,

For more modern mathematics, you can come to my office in the future. I wouldn’t mind giving you some learning materials in this area.”

Although Ling said this, she didn't expect anyone to really aim at becoming a mathematician. People with that kind of ambition should apply for Heimdall Academy instead of Thorz Military Academy.

"Today's first lesson starts with mechanics and mathematics. Everyone turns to the first chapter of the lecture notes. The content of this chapter is very simple. We are discussing units. For mathematical applications, any calculation must be based on units.

The unit for measuring land is the square Sel moment, the unit for counting the population is the household, and the monetary unit for buying things is the milla. The unit is the name of the standard quantity for measuring things. It is generally divided into setting units and physical units. If it is the main

Day school graduates should all have been exposed to elementary physics. But I hope everyone can understand the chain rule. Some people who have studied calculus by themselves probably understand what I am talking about. I will teach the course on differential equations next month, and even if not

It doesn’t matter if you know it. Because mechanical mathematics is much more intuitive than pure numerical mathematics and is not that difficult to understand.”

Calculus is not within the scope of the unified Sunday school graduation examination, so many people have not studied it specifically.

"We are accustomed to assign the properties of physical quantities to phenomena that can be analyzed qualitatively and quantitatively in reality. Except for pure numbers, all physical quantities have a dimension and a unit. And we can perform operations on the units. For example

, if you ask how many seconds there are in a year... Of course, I know you will know how many seconds there are immediately. But I hope you will calculate it in the following way."

Ling began to write on the blackboard with chalk. (The inside represents the content of the blackboard.)

1 year = 1 (year/day) x day

"The formula I wrote is obviously correct, because the two 'days' will cancel each other. After that, continue to write 'hours'."

1 year = 1 (year/day) x (day/hour) x hour

"So far, this equation still holds true. Ah, the reason why we use days instead of months is because the number of days in each month is different. As for the students who want to complain that leap years will have one more day than other years... In fact,

If I asked you how many days there are in ten years, would you answer me 3650 days or 3652 days? Although this is not rigorous, in a sense it is the consensus on the continent of Samlia. Back to the topic, in Eq.

Add 'minutes' after the word, and 'seconds' at the end."

Ignoring the students who were expressive due to the interesting lecture, Ling continued to write on the blackboard at her own pace.

1 year = 1 (year/day) x (day/hour) x (hour/minute) x (minute/second) x second

"This is important. Because if you treat the units as numbers, they can cancel each other. Now you can immediately know that 1 (year/day) = 365, because 1 year = 365 days. In the same way, 1 (

Day/hour)=24, 1(hour/minute)=60, 1(minute/second)=60. Keep dividing seconds in this way. The formula will become as follows."

1 year = 365x24x60x60x seconds

"Of course, this is a very simple example. Some may ask why it is so unnecessary? I think this shows you how to deal with units correctly. You should still pay attention to this rule when you encounter complex problems. Dimensions

Analysis can help you analyze the correctness of the solution. With the correct ideas, you will not be in a hurry when you encounter more complex units in the future. Is there anything you don’t understand so far?”

After ten seconds, no one asked any questions, and Ling assumed that everyone understood her intention.

"We will adopt the mks unit system in the future. mks means the acronym of meter-kilogram-second. In fact, fifty years ago, Semley

The prevailing unit system in Asia is still the cgs unit system (cm-g-s). Of course, it is closely related to the mks unit system, but after the guidance revolution, everyone began to use the mks unit system. Don’t ask me,

I don’t know why. Changes in tradition are often spontaneous behaviors of human beings. This should be the topic of Instructor Henry’s politics class instead of our math class. Is it more convenient? There is indeed this view. But, human beings always

I feel that things I am used to are more convenient. I am used to the mks unit system, so I find the mks unit system convenient. But for people who lived fifty years ago, the cks unit system may be more convenient."

After answering the students' questions, Ling suddenly thought of Yorugu, who is now 74 years old. It seems that he still likes the cks unit system very much.

"Next, an important concept that you must remember is significant digits. This concept has a different meaning in pure mathematics, but it is crucial in mechanical mathematics. Specifically, when I write a numerical value as

When referring to the physical quantity 2.33, I need you to understand that it is not equal to 2.3300."

2.33≠2.3300

"Although in pure mathematics, both sides of the equation are equal, in mechanical mathematics, when I write 2.33, it refers to between 2.32 and 2.34. And 2.3300 refers to between 2.3299 and 2.3301

.In other words, when you record any physical quantity, there is an uncertainty of ±1 in the last digit. So the two numbers are roughly equal, but the right side is much more precise. The significant digit on the left side is the second decimal place,

The significant figure on the right is the fourth digit. If you add units to the equation, maybe you can see it more intuitively."

2.33kg≠2.3300kg

2.33kg=2.33kg±0.01kg

2.3300kg=2.3300kg±0.0001kg

"I can also write 2.33 as 233x10^-2, and obviously the two numbers are equal."

2.33=233x10^-2

"This equation is equal in pure mathematics and mechanical mathematics. Because the last digit has an uncertainty of ±1. But don't misunderstand, 233x10^-2 is not equal to 23300x10^-4 in mechanical mathematics.

.The reason lies in the significant figures. Next you can read the part about significant figures in the handout."

The content was not very advanced, but half of the students frowned. It was probably because it conflicted with their past stereotypes. Ling was not in a hurry and gave them a few minutes to rest.

She walked up to Tova and asked, "How is it? It should be very basic content for you."

"Ah, no...the teacher in Sunday school never mentioned these contents at all. I think these are basic, but very important."

"It is indeed very important. It can be said to be the basis of any applied research. It would be great if everyone could be as keen as you."

"Hey, if there are classmates who can't keep up, I will try my best to help them."

"Well, are you the legendary good old man?"

"No, it's nothing."

After chatting lightly with Towa, Ling returned to the podium.

"I just used Krim as an example, so let's talk about Krim's definition. Weight is not equal to mass. In daily language, the two are often confused. In daily life, we often say xx 'weight' xx grams

rim, but academically we need to make a strict distinction. When you say something is x krim, what you are saying is that its 'mass' is x krim. It and the number of microscopic particles that make up the matter

Related. Molecules, atoms, electrons, gluons, yonons, lutons, and yonons, including all of them, are mass. Quality can be said to be an intrinsic property of any substance, even the air that each of us is accustomed to.

, each cubic submoment of air also has a mass of 1.29 Krim. So mass is a measure of a total quantity, and 'heavy' is a measure of force. Gravity is a measure of the stress an object experiences in a specific gravitational field.

.When you say you weigh 50 krims, what you are referring to is that the attraction of the earth beneath your feet is 50 krims. The two concepts are closely related but not the same. I will discuss it in the classical mechanics of the day after tomorrow.

The section on the Three Laws will further discuss this. The content I am talking about now belongs to the knowledge that can be accessed by senior students in Sunday school, so I will assume that everyone here has no questions."

Even though Thorz was an inferior student, he was probably one of the best in the entire university. He probably didn't have a zero-level student like Fei, so Ling felt that she didn't need to teach it all over again.

"Actually, at the end of each class handout, there is a section called Review and Summary. In order to test your mastery of knowledge, you can read this section after class. If you can understand all the contents of this section

, you will have mastered the essence of this chapter. I have also arranged some exercises in the handout. This is not an assignment, and you are not required to complete it. When you feel that you have mastered it, try that one. If there is no problem, then

That's it. Mathematics classes are three times a week. I will assign ten questions at the end of the first class every week, covering the knowledge points that will be taught this week. They will be handed in before the first class of the next week. No homework will be handed in.

, this week’s grades are gone. If my usual grade accumulation is too low, I will be disqualified from taking this midterm exam and final exam. As for copying homework without asking for explanations... Hehe, you are free to do so, but I think among you

There shouldn’t be anyone so stupid.”

After a slight warning, Ling began the second section, a straight-line movement.

Before explaining, Ling first inserted a section on pure mathematics and briefly introduced derivatives.

Instead of using simple formulas from Sunday school, we directly use derivatives to calculate instantaneous velocity to calculate linear motion. This is to gradually put aside past problem-solving habits through practical practice.

Different from the first section, the second section involves more calculations. However, Ling did not pay attention to the comments made by some students and continued to explain in simple and profound terms. In her words, when she did not understand, she felt that it was too high.

It’s hard to climb, but once you understand it accurately, it will feel natural.

The lecture lasted forty minutes, followed by a ten-minute break. The next forty minutes were Q&A time. Students who had no questions could finish the class and leave the lecture theater directly after completing an exercise. Those who had questions would continue to explain.

.

After she made all the students understand the content of the second period, the bell rang for the first period.

Although the first day of classes was basically relatively simple, this was just the beginning of the nightmare for all members of the 220th class of Thorz.


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