### Answers (63)

 4 Prove Cauchy's inequality: $(\sum_{i=1}^n a_i b_i)^2 \le \sum_{i=1}^n a_i^2 \sum_{i=1}^n b_i^2.$ 4 example for calculation of the exterior derivative 3 Trick/Fake proof of 2x2=5 ; algebraic form 3 When can I say that $A=\text{cover of A}$? 2 Evaluating power series

### Reputation (1,819)

 +2 Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$ +2 Complex number lemma +20 How to derive Bernoulli's theorem for an elastic fluid from Lamb's equation +10 Poiseuille flow: can I avoid the simplification that $u=u(y)$?

### Questions (45)

 6 Problem in the theory of finding the unique solution of $-u'' = \delta_0$ and $-u'' + cu= \delta_0$ 5 Poiseuille flow: can I avoid the simplification that $u=u(y)$? 4 How to solve explicitly the Dirichlet problem (in dimension 2) with boundary data $f(e^{i\theta}) := ( \sin(\theta) - \cos(2\theta))^2$ 3 A different music “shuffle” feature 3 Suppose $f,g$ are two absolutely continous functions in an interval $[a,b]$. Show $fg \in AC[a,b]$.

### Tags (104)

 11 calculus × 13 5 derivatives × 6 7 real-analysis × 9 5 elementary-set-theory × 4 7 algebra-precalculus × 4 4 integration × 9 6 probability × 7 4 limits × 8 5 solution-verification × 6 4 measure-theory × 7

### Bookmarks (56)

 391 The Ring Game on $K[x,y,z]$ 151 Pythagorean triples that “survive” Euler's totient function 48 Wild automorphisms of the complex numbers 47 Prove/disprove $(\int_0^{2 \pi} \!\!\cos f(x) \, d x)^2+(\int_0^{2 \pi}\!\!\! \sqrt{(f'(x))^2+\sin ^2 f(x)} \, dx)^2\ge 4\pi^2$ 39 If there are $74$ heads and $196$ legs, how many horses and humans are there? [closed]

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