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Jichao
  • Member for 13 years, 9 months
  • Last seen more than a month ago
  • China
218 votes
21 answers
159k views

Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx$

183 votes
17 answers
168k views

How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?

49 votes
21 answers
8k views

Could you explain why $\frac{d}{dx} e^x = e^x$ "intuitively"?

45 votes
3 answers
5k views

Is there any connection between Green's Theorem and the Cauchy-Riemann equations?

34 votes
4 answers
44k views

How to prove that the derivative of Heaviside's unit step function is the Dirac delta?

31 votes
6 answers
23k views

An intuitive explanation of the Taylor expansion

24 votes
3 answers
8k views

Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?

19 votes
2 answers
11k views

Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function

18 votes
4 answers
63k views

What does smooth curve mean?

12 votes
7 answers
19k views

Why do we need vectors and who invented it?

12 votes
5 answers
21k views

Difference between one-variable calculus and multi-variable calculus?

12 votes
8 answers
3k views

What's the hard part of zero?

11 votes
4 answers
6k views

Could you a give a intutive interpretation of curl?

9 votes
5 answers
26k views

What's the geometrical interpretation of the magnitude of gradient generally?

8 votes
4 answers
571 views

Prove inequality: When $n > 2$, $n! < {\left(\frac{n+2}{\sqrt{6}}\right)}^n$

8 votes
2 answers
246 views

Prove that $ \frac{n^2}{\sum_1^n{\frac{1}{a_i}}} $ is convergent.

8 votes
6 answers
6k views

Example of a trigonometric series that is not fourier series?

7 votes
8 answers
4k views

How many ways are there to define sine and cosine?

7 votes
2 answers
3k views

Help understanding the definition of tangent vector or tangent plane?

7 votes
2 answers
804 views

How to prove that this set is closed?

7 votes
2 answers
1k views

Can you conjecture what functions $f: \mathbb{R} \to \mathbb{R}$ is continuous when considered as maps from $\mathbb{R}$ to $\mathbb{R_\mathcal{l}}$?

6 votes
3 answers
357 views

How to calculate $\lim_{x \to 0}\left(\frac1{x} + \frac{\ln(1-x)}{x^2}\right)$?

6 votes
3 answers
1k views

Explain why calculating this series could cause paradox?

5 votes
3 answers
1k views

Book recommendation on the history of PDE/ODE?

4 votes
3 answers
10k views

How to prove DeMorgan's law?

4 votes
2 answers
133 views

algorithm transfer one coin matrix to another coin matrix

3 votes
1 answer
3k views

What's wrong with my calculation for checking the divergence law?

3 votes
6 answers
5k views

Calculating $\oint_{L} \frac{xdy - ydx}{x^2 + y^2}$

3 votes
6 answers
6k views

Could you recommend some classic textbooks on ordinary/partial differential equation?

2 votes
1 answer
214 views

Why we assign $1/2[f(\epsilon+0) + f(\epsilon-0)]$ as the value at the discontinuity point?