I would like to obtain the magnitude of a complex number of this form: $$z = \frac{1}{\sqrt{\alpha + i \beta}}$$ By a simple test on WolframAlpha it shoul...

Apparently, it can be shown that the Cauchy-Riemann equations can be written simply as, $df/dz^*=0$. I do not understand how it does not immediately follo...

Proposition 21. Let $\varphi$ be the Cantor-Lebesgue function and define the function $\psi$ on $[0,1]$ by $$ \psi(x) = \varphi(x) + x \quad \text{for all...

Let $T : \Bbb R^2 \to \Bbb R^3$ given by $$T((x_1, x_2)^T) = (x + 2y, 2x - 5y , 7y )^T$$. We have $T((0, 1)^T) = (2, -5, 7)^T$ and $T((1, 0)^T) = (1, 2, 0...

So, I have finished study for linear equations for my methods course but now I have run into a problematic quadratic equation. I have tried researching fo...

Translate the following argument into symbolic form. State clearly what each of the propositions are I walk and I cycle and I run. If I do not stay at hom...

Salutations, I have been trying to approach an ODE with trigonometric functions that I found interesting: $$y'+x\sin(2y)=xe^{-x^2}\cos^2(y)$$ I tried...

Let’s say for example you want to evaluate this integral: $$\int_0^{\pi/2} \sin(x)\cos(x)\,dx$$ The best way to do that is to use a substitution, namely y...

I was wondering if for the below matrix multiplication: $A^T * A *\ A^{-1} * (A^{-1})^T$ we can assume the product of the inner 2 matrices to equal the id...

I have a volume $V$ bounded by the following equations: $ x^2 + y^2 + z^2 = 1 $ $ z^2 = (x^2 +y^2) {\sqrt2} $ and I have to find out the mass of the volum...