Ryker
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### Questions (25)

 11 How to go about studying chaos theory/dynamical systems/fluid dynamics in grad school with a physics background? 7 Why is $x^2$ +$y^2$ = 1, where $x$ and $y$ are complex numbers, a sphere? 6 Is it easier to publish in certain areas of mathematics? 6 Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$ 4 Given independent solutions $f(x)$ and $g(x)$ of a linear homogeneous DE on $(a,b)$, which must also be solutions?

### Reputation (528)

 +5 How to go about studying chaos theory/dynamical systems/fluid dynamics in grad school with a physics background? +15 Show that $\lim_{r\to 0} \frac{1}{r^2}\int_{C_{r}}f(z)dz = 2 \pi i\frac{\partial f}{\partial \bar{z}}(z_0)$ +5 What is $\frac{\partial z}{\partial y}$ for $z = F(u, v, y), u = f(v, y)$ and $v = g(x, y)$? +5 Show that Möbius transformations that preserve the unit disk are of the matrix form $\tiny \begin{bmatrix}a & b \\ \bar{b} & \bar{a} \end{bmatrix}$

 4 If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$ 1 What is a Boolean Function? 1 Setting up an integral question 1 Intersection of a manifold with open set 1 Integration by parts : $\int 2x \cos(x^2 + 1) dx$

### Tags (44)

 4 inequality × 3 1 volume 4 proof-verification 1 boolean-algebra 2 integration × 2 1 logic 1 multivariable-calculus 0 real-analysis × 5 1 manifolds 0 complex-analysis × 4

### Accounts (10)

 Mathematics 528 rep 315 Academia 176 rep 5 Physics 170 rep 5 Mathematica 145 rep 5 Philosophy 111 rep 4