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10h
awarded  Constituent
Dec
16
comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
Yes, sorry - question updated. Thanks for spotting this.
Dec
8
awarded  Caucus
Dec
7
awarded  Nice Answer
Dec
3
comment Summation of logarithms
You have $$S=\sum_{k=1}^n\log(a-x_k)=\log\prod_{k=1}^n(a-x_k).$$ So $$\prod_{k=1}^n(a-x_k)-e^S=0.$$ So you need to be able to solve equations of the form: $$\prod_{k=1}^n(a-x_k)-c=0,$$ where $c$ is some constant.
Nov
26
awarded  Notable Question
Nov
20
comment Finding the roots of $x^2+(3+5i)x+(7+11i)=0$
Re polar exponential form - see my answer below for the answer.
Nov
20
revised Finding the roots of $x^2+(3+5i)x+(7+11i)=0$
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Nov
20
revised Finding the roots of $x^2+(3+5i)x+(7+11i)=0$
added 542 characters in body
Nov
20
answered Finding the roots of $x^2+(3+5i)x+(7+11i)=0$
Nov
19
comment Most ambiguous and inconsistent phrases and notations in maths
Since I used $\log$ instead of $\text{Log}$ and I did not specify a branch then to me this is clearly a mistake.
Nov
19
comment Most ambiguous and inconsistent phrases and notations in maths
@Mariano Suárez-Alvarez The notation $\text{Log}$ is also sometimes reserved for the principal branch, often when $\log$ for the (general) multi-valued function is used. In whichever context, I've seen this cause confusion in obtaining results.
Nov
15
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
In fact: $e^{ix}=\cos(x)+i\sin(x)$.
Nov
13
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
Good point. I think at the time I "understood" what numbers were, but these new numbers (complex numbers) were so strange, and were presented with the added "imaginary" verbiage that they were mesmerizing to me! Of course later I realised that complex numbers are not complex at all and that there is absolutely nothing imaginary about the idea of $i$. Complex numbers are a system of numbers which obey a certain set of rules in a consistent way. But I'm pleased to have been captivated :-)
Nov
11
comment The Integral of Multiple Tangent Functions
Try increasing the working precision: Integrate[..., WorkingPrecision->100].
Nov
11
revised Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
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Nov
11
comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
So it's down to the method used to compute the derivative. Need to be judicious with tools.
Nov
10
accepted Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
Nov
10
revised Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
added 1 character in body
Nov
10
comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
Mathematica is great, but it does have bugs. I've found at least 5 so far in my life time of using it. From infinite summations, to sum convergence conditions, to this !! I've filed another bug report with Mathematica ;-)