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1d
answered How to calculate the exponential of a matrix?
May
11
comment How to do this integral.
@DanielFischer Ahh right; thanks for explaining that, I'm familiar with $\mathrm{p.v.}$ for the principle value of functions, but I'd never seen $\mathrm{v.p.}$ before! I understand what you mean now, thank you!
May
11
reviewed Reject How to do this integral.
May
11
comment How to do this integral.
@DanielFischer I'm rather intrigued, as the integral is undefined for real $k$ (as illustrated by GEdgar), so how does this technique work and what does it "mean"? Also, I've never seen a $\mathrm{v.p.}$ before an integral before - What does that mean?
May
11
comment How to do this integral.
@DanielFischer I'm not sure whether this will be useful to you (I've never studied complex analysis), but Mathematica reports the answer to be: $$\frac{p}{p^2-k^2},\qquad |\Im(p)| < \Im(k)$$
May
7
revised Describing groups with given presentation? $\langle x,y\ |\ xy=yx,x^5=y^3\rangle$ and $\langle x,y\ |\ xy=yx,x^4=y^2\rangle$.
added 26 characters in body; edited title
May
5
revised Find the standard matrix representation of the linear transformation T in M2,2
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May
5
comment Represent the transformation with respect to the standard basis
This is in the standard basis where our basis vectors are $\hat{\boldsymbol{e}}_{1} = \begin{pmatrix}1 & 0\end{pmatrix}^{T}$ and $\hat{\boldsymbol{e}}_{2} = \begin{pmatrix}0 & 1\end{pmatrix}^{T}$ as we are implicitly writing the vectors with the known transformations as linear combinations of the standard basis vectors. (i.e. $\begin{pmatrix}1 & 3\end{pmatrix}^{T} = \hat{\boldsymbol{e}}_{1} + 3\hat{\boldsymbol{e}}_{2}$
May
5
answered Represent the transformation with respect to the standard basis
May
5
revised Real analysis question about differentiation
added 69 characters in body
May
1
reviewed Edit Factorial Proof Problem
May
1
revised Factorial Proof Problem
formatting
May
1
comment Factorial Proof Problem
Beautifully simple, +1
Apr
30
revised What did Alan Turing mean when he said he didn't fully understand dy/dx?
added 36 characters in body
Apr
30
revised Evaluating $\int_{-5}^5\int_{-5}^5-\frac{3}{2}|x+y|-\frac{3}{2}|x-y|+15\,\mathrm{d}x\,\mathrm{d}y$
added 198 characters in body
Apr
30
revised Evaluating $\int_{-5}^5\int_{-5}^5-\frac{3}{2}|x+y|-\frac{3}{2}|x-y|+15\,\mathrm{d}x\,\mathrm{d}y$
added 18 characters in body; edited title
Apr
26
revised What properties does $A\to B$ satisfy under 1-1 correspondence?
added 39 characters in body
Apr
24
revised How to calculate $\int_{C(0,1)}\frac{\sin z}{z^4}dz$
added 10 characters in body; edited title
Apr
24
revised Dirichlet integral using real Analysis
added 48 characters in body; edited title
Apr
22
comment given that ${\log_9 p} = {\log_{12} q} = \log_{16}(p+q)$ find the value of $q/p$
Does $\,^{3}\log(n) = \log_{3}(n)$ in your question? Where $\log_{3}(n)$ is log base 3?