I Kidnapped An Alien Civilization

2021-07-07

Chapter 69 Early Graduation Exams

“Li Mo, your application for early graduation has been received. The Academic Affairs Office of the Department has researched and decided to test you in the 5th lecture hall on Wednesday and Thursday. I hope you will take the test on time.”

Seeing the letter in the mailbox, Li Mo sighed in relief, after the test, he said You can directly graduate and participate in research projects in advance.

Although Li Mo was confident to pass the exam, he went to the corner of the library to review all the subjects again.

“Li Mo, have you decided to graduate early?”

Li Mo turned around and saw Ying Sa Sa standing behind him with a frown.

“Yes, the Academic Affairs Office has approved my application, and the exam will be held this week.” Li Mo said calmly.

Ying Sa Sa hearing this with red eyes, “Then are you going to study abroad, can we meet again?”

Li Mo looked slightly startled, with a trace in the corner of his eyes With a smile, “I’m ready to apply for Professor Wu’s graduate school and will continue to stay at Yanda University.”

“Really, that’s very good.” Ying Sasa was overjoyed, perhaps realizing her loss Self-control, she said a little embarrassedly: “Then you continue to read the book, and I will help them deliver the book.”

WeChat

Zhou Dayong: “The installation workers have entered the site, and Brother Qiu and I are watching the scene.”

Li Mo thought for a while and replied To: “Thank you, the installers must follow the blueprint.”

Zhou Dayong: “Received!”

“There are two bodyguards supervising the work on site, so maybe I can relax my mind. Right.” Li Mo felt that he was a little weak, as the saying goes: “I’m covered in iron, how many nails can you hit?”.

On Wednesday morning, the 5th lecture hall.

Li Mo came to the classroom on time. In the empty classroom, there was only a teacher from the Academic Affairs Office with the exam papers and a graduate student who was temporarily arrested. .

“Li Mo Junior Brother, I’m Professor Wu’s graduate student, Zhou Ming.” The boy with glasses greeted shyly.

Li Mo smiled comfortably and said, “It’s a coincidence. I’m preparing to apply for Professor Wu’s graduate school. Maybe you will be my Senior Brother in the future, please take care of me.”

Zhou Ming said humbly: “Your name has long been spread throughout Yanda University. Professor Wu praised you as a rarely seen math genius in front of us.”

” I won an award, I won an award.”

“cough, cough”, the teacher at the Academic Affairs Office saw that the two of them were actually doing their homework, and interrupted, “Because the time is tight, let’s start the exam now, Li Classmate Mo.”

“This morning is expected to be an exam for 3 subjects, “Mathematical Analysis”, “Advanced Algebra” and “Calculus Equation”. Because it is an early exam, it is not according to the normal exam time Go ahead.”

“You can just hand me the 3 completed test papers before 12 noon.” He then handed out the 3 test papers.

The first test paper is “Mathematical Analysis”,

1. Leaf-shaped line x=2t-t, y=2t-t, 0≤t≤2, find this curve The enclosed area of the graph.

This is too simple, Li Mo came to the answer after a little thought, he wrote shua shua on the test paper:

|y=tx, t 0 0.5 1 1.5 2 x 0 0.75 1 0.75 0 y 0 0.375 1 1.125 0, area A=∫<0,1>(2t-t^41022)(2-2t)dt =∫<0,1>(4t-6t^2+ 2t^3)dt =(2t^2-2t^3+t^4/2)|<0，1>=1/2.

2.u=(x/y)^( 1/z) all partial derivatives at (1, 1, 1).

This question is not difficult for him. In less than 2 seconds, Li Mo deduced the answer:

u=u(x, y, z)u/x=[ (x/y)^5261(1/z)]/(zx)=u/(zx)u/y=-[(x/y)^(1/z)]/(zy)=-u/( zy)u/z=-[(x/y)^(1/z)](1/z)ln(x/y)=-u[ln(x/y)]/zu=(x/y) ^(1/z) at (1, 41021, 1) 1653u=u(1,1,1)=1 u/x=1, u/y=-1, u/z=0

3. To find the total differential of u=ln(sin(xy))

1 second, it only took 1 second, Li Mo wrote the answer directly.

du=(u/x)dx+(u/y)dy u/x=y[cos(xy)]/[sin(xy)]u/y=x[cos(xy)] /[sin(xy)] du=(ydx+xdy)[cos(xy)]/[sin(xy)]

In just 30 minutes, Li Mo finished the exam paper of “Mathematical Analysis” , if it weren’t for the open-ended question at the end, he used 6 methods to explain it, and it could be faster.

The next paper is Advanced Algebra.

1. Let V1 and V2 be the solution spaces of homogeneous Simultaneous Equations x1+x2++xn=0 and x1=x2==xn respectively, find V1, V2 and prove P^n=V1+ V2, where P^n is an n-dimensional vector space on the number field p.

Answer: V1 is the orthogonal complement space of the vector bai(1, 1, ., 1), the base is (1, -1, 0, 0, ., 0), (du1, 0, -zhi1, 0, …, 0), . . . , (1,0,…,-1), the first component of each vector is 1, the k+1th component is -1, and the remaining components are 0, k=1,2,. . . , n-1. The basis of V2 is (1, 1, 1, ., 1). It is easy to see that V1 and V2 are orthogonal (the basis vectors are orthogonal), the dimension of V1 is n-1, the dimension of V2 is 1, and the sum of the two is n, so the two subspaces have The sum is a straight sum, which happens to be the full space.

1 minute to complete the first question. Since spiritual wisdom has risen to Level 2, he feels that he can easily grasp the problem-solving ideas.

Zhou Ming next to him saw that Li Mo had completed the “Mathematical Analysis” test paper, so he could not help but walk behind him and read it. I saw the immature teenager in front of me, starting a topic like writing an article, chalking extremely fast.

Even if he encounters a tricky question, the boy frowns slightly, and he can solve it with a little thought.

Professor Wu often boasted in front of himself that there was a genius in the Department of Mathematics, but Zhou Ming didn’t believe it. Anyone who can enter the Mathematics Department of Yanda University is not a genius.

But now that Zhou Mingcai really understands the meaning of genius when he sees the young man in front of him who is doing the questions quickly.

The “Advanced Algebra” test paper was also quickly completed by Li Mo. Zhou Ming subconsciously looked at his mobile phone, and it only took 20 minutes.

The next test paper is Calculus Equation, which is known for being computationally intensive. It’s not the kind of problem that can be easily solved with a problem-solving idea.

“How long will it take to see you this time?” Zhou Ming deliberately looked at his mobile phone this time. It was 9:30.

The first question, let a, b, c are all positive numbers, and y(x) is a solution of the differential equation ay”+by’+cy=0, prove:

lim(n~+∞)y(x)=0.

Li Mo quickly calculated it in the heart and wrote:

ar^2+br+c=0

Because a, b, c >0

The two roots are r1, r2

By Weida’s theorem

r1+r2=-b/a<0

r1*r2=c/a>0

If r1 and r2 are real roots, then bai is obviously only r1, r2<0 can satisfy du and less than zero zhi, and the product is greater than zero

When x->positive infinity, exp(r1*x), exp(r2*x)->0, so if y->0

is a complex root, it must be a conjugate complex root, Because the coefficients are real numbers

so r1=m+in, r2=m-in

r1+r2=2m=-b/a<0

because m<0

exp(mx)->0 when x->positive infinity

|C1 cos n x+C2 sin nx|<=|C1|+|C2|Yes bounds

so when x->positive infinity y->0

in summary lim(n->+∞)y(x)=0

good It’s long, and my hands are very tired. The title of the Calculus equation is known for its tediousness. Li Mo cheered up.

Track 2.Track 3.Track 4.

Finally over, Li Mo wrote the last math symbol on the test paper.

Zhou Ming looked at his phone again. At 9:55, it took 25 minutes, and the young man in front of him completed the set of test papers that he needed at least 2 hours to complete.

“teacher, I’m done, can I submit the papers in advance?” Li Mo asked with his hands up.

“Finished?” The teacher at the Academic Affairs Office, who was in a daze at the door, was a little surprised. That was three exam papers. It was planned to test him after finishing the exam in one morning.

didn’t expect he did it so quickly.

The teacher from the Academic Affairs Office came over, sorted out his test papers and put them in a sealed bag.

(End of this chapter)