1,912 reputation
423
bio website cnblogs.com/misaka01034
location Shanghai,China
age 20
visits member for 2 years, 8 months
seen 2 days ago

I'm a senior undergraduate student in Shanghai Jiao Tong University Zhiyuan College majoring in mathematics. The website given on the left is my notes and some personal view of mathematics( in Chinese ). I'm trying to learn as more as I can at the undergraduate process.

As Confucius said:

"If I am walking with two other men, some of them will serve as my teacher. I will pick out the good points of the one and imitate them, and the bad points of the other and correct them in myself."("三人行,必有我师焉。择其善者而从之,其不善者而改之")

This website contains n people, and from each 2 of them there is at least one man that will serve as my teacher, thus there at least n-1 teachers. This is a good place since are so many teachers here that may teach me mathematics!


Dec
9
awarded  Caucus
Nov
17
comment Existence and uniqueness of an integral equation
That's a great answer! Thanks a lot!
Nov
17
accepted Existence and uniqueness of an integral equation
Sep
22
awarded  Notable Question
Sep
12
accepted Homework: Solve the poisson equation in the outer sphere
Sep
12
comment Homework: Solve the poisson equation in the outer sphere
Thank you Felix. The $g$ here is not a constant, but a function depend on the position. Apologize for not responsing your comment, since I've got the answer for the question long ago.
Aug
28
comment Is true the boundary of compact set of $\mathbb{R}^n$ have Measure Zero?
Also, the boundary of Mandelbrot set is of dimension $2$.
Aug
27
revised complex integration-how to solve the given problem
added 223 characters in body
Aug
27
comment Evaluation of $\begin{align} \int^{\infty}_{0}\end{align} \dfrac{1}{1+x^n}dx$ with the use of Residue theorem
Here is what you need. Maybe this post should be marked as duplicate?
Aug
27
comment Evaluation of $\begin{align} \int^{\infty}_{0}\end{align} \dfrac{1}{1+x^n}dx$ with the use of Residue theorem
You may consider two cases, one for $n$ to be even and one for $n$ to be odd.
Aug
27
comment Area of the region bounded by graphs of two exponentials.
OK, sorry that I was wrong, you are correct!
Aug
27
comment Area of the region bounded by graphs of two exponentials.
I think the integration now should be $\int_{0}^{0.59} \pi(e^{-x^2}-2x^2)^2dx=0.978763$. How do you get $0.4203$?
Aug
27
comment Evaluation of $\begin{align} \int^{\infty}_{0}\end{align} \dfrac{1}{1+x^n}dx$ with the use of Residue theorem
@AlexyVincenzo Unless $\exp(2\pi i/n)=1$, you can use the summation formula, since the proof is easy.$1+z+z^2+\ldots+z^n=f(z)$, then $zf(z)-f(z)=z^n-1$, the formula follows as Yssub pointed out.
Aug
27
answered How to get this inequality
Aug
27
comment Area of the region bounded by graphs of two exponentials.
The primitive of $e^{-x^2}$ is not an elementary function, so this cannot be integrated by hand anyway. See Liouville's theorem
Aug
27
answered complex integration-how to solve the given problem
Aug
27
comment Evaluation of $\begin{align} \int^{\infty}_{0}\end{align} \dfrac{1}{1+x^n}dx$ with the use of Residue theorem
Since $z_k$ is $\exp(2\pi i/n)$ times of $z_{k-1}$.
Aug
27
comment Evaluation of $\begin{align} \int^{\infty}_{0}\end{align} \dfrac{1}{1+x^n}dx$ with the use of Residue theorem
Since $\sum \frac{1}{n z_k^{n-1}}$ is a geometric sequence, you may simply use the summation formula for geometric sequence.
Aug
27
answered Area of the region bounded by graphs of two exponentials.
Aug
27
answered A Borel-Cantelli lemma exercise.