521 reputation
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location Bangalore, India
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visits member for 2 years, 5 months
seen 18 hours ago

I am a Christian. Although I have an abiding interest in science and philosophy, I view things from a distinctly Christian vantage point, which harmonizes human well-being with what we know of the natural world.

Here's a nice quote I came across:

"The spectacle of the universe seems all the more grand and beautiful and worthy of its Author, when one considers that it is all derived from a small number of laws laid down most wisely." -Maupertuis, 1746


Apr
12
comment Differential equation by series solution method: equating coefficients to zero
I think I got it. n=1,2,3.. and upwards already invoke n=0, which is set to 0. In other words, $2a_2$ is the coefficient of $x^0$, and we have to set coefficients of all powers of $x$ equal to zero.
Mar
31
comment How do you integrate $\int x(x+3)^ \left( 1/3 \right) dx$
The answer that I got, which is shown as correct is : $\frac{3}{7}(x+3)^{\frac{7}{3}}-\frac{9}{4} (x+3)^{\frac{4}{3}}$
Mar
31
comment How do you integrate $\int x(x+3)^ \left( 1/3 \right) dx$
I apologize for not being clear. I did substitute the $x$ with $u-3$, but the form of the equation seems similar. It didn't occur to me that the new form can be distributed, while the old one cannot.
Feb
2
comment What is the intuitive meaning of the basis of a vector space and the span?
Is there an upper bound on the number of matrices that can be used as a basis for $\mathbb R ^2$, like the one you have shown above?
Jan
22
comment Given $a=bc$ and $c\geq 1$ and $b\neq 0$, which is greater: $a$ or $(b+c)$?
$b$ is nonzero.
Sep
10
comment How do I calculate the quartiles for this problem?
There is some confusion between the answers by EpicGuy and Sim. My source agrees with the former, while the quartiles calculator at alcula.com/calculators/statistics/quartiles agrees with the latter. I would appreciate it if someone could resolve this.
Sep
10
comment How do I calculate the quartiles for this problem?
BTW, I am the OP. I was finally able to log into my own account.
Sep
10
comment How do I calculate the quartiles for this problem?
Your answer doesn't agree with the other answer posted by EpicGuy. It also doesn't agree with my original source from where I took the problem. I like your method, but the other answer is the correct one. I'd like to know how to get the correct answer using this method. Could you please double-check this? Thanks.
Aug
10
comment Intersection point of 2 circles
Sorry, what I meant was, you substitute out whatever's possible using the 2nd equation. So, for example, you could substitute using $x^2+y^2=100$ in the remaining equation, and the $x^2$ and $y^2$ terms disappear.
Jul
1
comment Regression towards the mean v/s the Gambler's fallacy
@GerryMyerson: Interesting. That's how Bayesian reasoning works, doesn't it?
Jul
1
comment Regression towards the mean v/s the Gambler's fallacy
"The only regression is that the coin is likely not to give such weird results in the next bunch of tosses."...Ah. Got it!
Apr
25
comment Should the sign be reversed if I square both sides of an inequality?
Similarly, I'd like to know how to square $x<y$ as well.
Mar
31
comment Find the median given a table of relative frequencies
I'm curious -- why do you think it should be zero? I don't see that.
Dec
7
comment Solving the time-independent Schrodinger equation for particle in a potential well
Ah, careless.. thanks.
Nov
22
comment Showing that $\langle p\rangle=\int\limits_{-\infty}^{+\infty}p |a(p)|^2 dp$
Thanks for your clarifications. That takes care of the $a(p')$. But what about the $p'$ becoming a $p$?
Nov
22
comment Showing that $\langle p\rangle=\int\limits_{-\infty}^{+\infty}p |a(p)|^2 dp$
Yes, but in the penultimate step, you have both $a(p)^*$ and $a(p)$ being integrated over $p$. This seems contrary to step 2, where $a(p)^*$ goes with $p$ and $a(p')$ with $p'$. So shouldn't your penultimate step read $\int_{-\infty}^{\infty} p' a(p)^*a(p') \, dp$?
Nov
22
comment Modulus of a complex function: $\Psi(x)=A_0 e^{-kx^2} e^{i\alpha x}$
It seems to work, and I'll make a note of it in my notes, but I just wanted to make sure that it's the most general way to find the modulus. Somehow, I seem to have missed the class where they extended the idea of a modulus to cover complex functions. It's like a secret that everybody is in on except me!
Nov
22
comment Modulus of a complex function: $\Psi(x)=A_0 e^{-kx^2} e^{i\alpha x}$
Can I do $|\Psi|=[\Psi^* \Psi]^{\frac{1}{2}}$?
Nov
22
comment Showing that $\langle p\rangle=\int\limits_{-\infty}^{+\infty}p |a(p)|^2 dp$
Also, I don't understand why you introduced the primed variables only to drop them in the last 2 expressions.
Nov
22
comment Showing that $\langle p\rangle=\int\limits_{-\infty}^{+\infty}p |a(p)|^2 dp$
I don't understand how you got the expression for $\Psi^*$. Can we simply take the conjugate within the integral sign? Does this mean that the integral of a conjugate is equal to the conjugate of the integral?