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 Yearling
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3h
revised Solving a delay differential equation
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10h
revised Solving a delay differential equation
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10h
revised Solving a delay differential equation
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10h
revised Solving a delay differential equation
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10h
asked Solving a delay differential equation
1d
comment Why do you need absolute value when taking $\sqrt{\cos^2(x)}$
$\sqrt{\cos^2(x)}\neq\cos(x)$ for all $x$.
2d
revised Is it true that $|e^z|\le e^{|z|}$ for all $z \in \mathbb C$?
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2d
answered Is it true that $|e^z|\le e^{|z|}$ for all $z \in \mathbb C$?
2d
answered Product of terms involving complex exponents
2d
comment Prove that for any integer $n$, if $b^2$ divides $n$, then $b$ divides $n$.
$$b^2\mid n\implies n=b^2k=bbk=b\ell\implies b\mid n.$$
Feb
9
comment Proving that $\binom{n}{k}\binom{\smash{k}}{m}\binom{m}{r} = \binom{n}{r}\binom{n-r}{n-m}\binom{n-m}{n-k}$
Use the definition of the Binomial coefficient.
Feb
3
revised Compute the integrals using the residue theorem
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Feb
3
answered Compute the integrals using the residue theorem
Jan
31
comment Finding the value of this integral $ \int_{-\pi/4}^{\pi/4}{ (\cos{t} + \sqrt{1 + t^2} }\sin^3{t}\cos^3 {t})dt$?
Very nifty !...
Jan
31
comment Finding the value of this integral $ \int_{-\pi/4}^{\pi/4}{ (\cos{t} + \sqrt{1 + t^2} }\sin^3{t}\cos^3 {t})dt$?
You could split the integral into two terms. The first term should be easy to integrate. For the second, you may find $\frac{1}{2}\sin(2t)=\sin(t)\cos(t)$ useful.
Jan
30
comment why $\int{\cos({\pi}t)} dt = \frac{1}{\pi}\sin({\pi}t)$?
When something new is "added" we can assume the old rules will work, but often they don't work meaning there's more going on than we know. One way to think is to always remember that the rules we know at present are some special case of more general rules. So e.g. your statement $\int\cos(x)dx=\sin(x)+C$ is a special way of writing $\int\cos(1\cdot x)=\sin(x)+C$, but what if the $1$ were some other number $a$. What general rule is there to handle such cases? It's not as straight forward as the case when $a=1$.
Jan
27
comment Prove convergence of $\sum _{n=1}^{\infty }\sin(1/n)/n$
Since $1/n\to 0$ as $n\to\infty$, maybe you could consider $\sin(1/n)$ in a neighbourhood of $0$, e.g. $\sin(1/n)\to1/n$ as $n\to\infty$...
Jan
22
awarded  Yearling
Jan
22
comment Finding the result of an infinite sum
That's no reason to methodically downvote every element of a question though.
Jan
20
revised I need to solve $\phi (x,y) = \frac{2V}{\pi} \int_{0}^{\infty} \frac{\sin(kx)\cosh(ky) dk}{k\cosh(ka)}$
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