# All Questions

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### Images of some regions of the complex plane by given function?

I'm trying the draw the image of $A=\lbrace z\in \mathbb{C}:-1<Im((1+i)z)<1\rbrace$ by $f(z)=1/z$ and the one of $B=\lbrace z\in\mathbb{C}:|z|<1\rbrace$ by $f(z)=(z-1)^{-1}$. I've managed to ...
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### Family of “something very close to be a curve” over a curve $C$

Hartshorne (IMHO restrictive) definition of a curve: Definition of (complex) curve: A curve is an integral separated scheme of finite type over $\mathbb C$ of dimension $1$. (The definition of a ...
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### Boundedness of sequence of functions

Consider a sequence of continuous integrable functions $\{f_n(t)\}_n$ such that $\ast\ \displaystyle\lim_{n\rightarrow\infty}f_n(t)=0$ for all $t>0$ $\ast\ \{f_n(t)\}_n$ is such that ...
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### Probability of $2$ boys in a family.

In a family there are 3 children with minimum $1$ boy.What is the probability there are exactly $2$ boys in the family? I think I have to use combinatorics to solve this problem. I have solved some ...
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### Finding SD given mean, median, 25th and 75th percentile [on hold]

I have the data from 2009 till 2013. I would like to plot a graph using these figures but i lack the SD. so is there a way to find it? Mean: 3048,3292,3369,3348,3520 Median: 2800,3999,3020,3000,3200 ...
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### Efficient ways to evaluate an integral with a logarithm

Is the approximation in terms of series for the logarithm $$\log(z)= \sum_{n=0}^{\infty}\frac{2}{2n+1}\Bigl(\frac{z-1}{z+1}\Bigr)^{2n+1}$$ a good approximation if I replace this series inside the ...
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### Trigonometric Functions on a unit circle

I have to find all solutions for $\theta$ in the given range: $$tan (\theta) = \frac {-1}{\sqrt3}, -\pi \le \theta \lt 2\pi$$ I said that if $(x,y)$ is on the unit circle ...
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### Proving a mod b < a/2 when a > b > 0

Suppose that $a \gt b \gt 0$. How can one prove that $a$ mod $b \lt a/2$? I understand why is that happening: if $a$ mod $b \gt a/2$ that means that $a/b \lt a/2$ and $a/b$ has enough "space" to ...
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### Existence of unique solution on $(-\delta,\delta)$ for $f(x)=1+x+\displaystyle\int^x_0\sin(tf(t))dt$

The following was a question previously given in a test at my university: Show that there exists some $\delta>0$ for which there is a unique continuous function ...
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### A topic for seminar in finite group theory.

I am doing a course on "Structure of finite groups" and we have a choice of giving a presentation on topics related to the course, Course outline is as follows- I was thinking of O-Nan Scott ...
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### A question about the proof of a theorem in Representation theory of groups

My Question is about one part of the proof of theorem in the book "A Course in the Theory of Groups" by Derek J.S. Robinson. I highlight the part that my question is about. We know that if $G$ is a ...
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### Probability Distribution for a Weird Card Game

I promise this is not for a homework problem, even though this sounds like only something a professor would dream up. Here is the game: I begin with a deck of 13 cards: 1 through 10, Jack, Queen, and ...
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Let $u$ be harmonic on $\{|z|<1+\epsilon\}$ for some $\epsilon>0$ and $u \geq 0$ on $\{|z|=1\}.$ Could anyone advise me how to show $\dfrac{1-|z|}{1+|z|}u(0) \leq u(z) \leq ... 0answers 17 views ### Nondimensionization of a simple system. A damped spring mass system is modelled below: $$m\frac{d^2y}{dt^2}=F_s+F_d\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space t>0$$ ... 1answer 16 views ### How to prove that a set of connectives is adequate I have this Table: $$\begin{array} {|c|} \hline A & B & A*B\\ \hline 1 & 1 & 0\\ \hline 1 & 0 & 1\\ \hline 0 & 1 & 1\\ \hline 0 & 0 & 0\\ \hline \end{array}$$ ... 0answers 14 views ### How to evaluate a line integral over the lemniscate of Bernoulli Evaluate the integral over the$\int_c$|y| ds where curve c is given by the equation$(x^2+y^2)^2=40^2(x^2-y^2)\$ I used polar coordinates but keep getting 0 as a answer. Help?

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