Does the equation Sqrt(x) + 1 = 0 have a solution? I would say that it doesnt. But the equation x^2 + 1 = 0 doesn't have a solution either, unless you define the imaginary unit i as the solution to the equation.
So why don't one define some unit which is the solution to the equation Sqrt(x) +...
My question pretty much is the title of this post, but let me explain it a bit more. When in physics or mathematics, or some other discipline involving math, you run into an integral, a differential equation or some other expression, how do you know if it's solvable or not? I mean, how do I know...
What am I doing wrong here, I thought the order of integration and differentiation didn't matter in most cases:
\int_a^b \frac{d}{dx} f(x) dx = \frac{d}{dx} \int_a^b f(x) dx = \frac{d}{dx} (F(b) - F(a)) = 0
This is zero no matter what the expression of f(x) because F(a) and F(b) are...
Hey!
I have always learned that functions like logarithms, exponentials, trigonometrics etc. have to operatore on pure numbers and not numbers with units. For instance, you cannot write:
Sin ( 5 kg*m/s^2 )
But in chemistry I often find formulas where logarithmes of numbers with units...
Can someone help me show the following:
\int_0^{\infty}r^k e^{-a r} dr=\frac{k!}{a^{k+1}}
I tried to use the polynomial expansion of e^x:
\sum_{n=0,1...} \frac{x^n}{n!}
...but I get stuck pretty fast. Can someone give me a few hints?
Thanks!
Just a question about the destruction of the euler equation that Data talked about. If pi was defined as the ratio between circumference and radius wouldn't that mean something for cos and sin also? So that cos(\pi)= 1 and sin(\pi)=0, and the euler formula therefore is preserved? Or am I...
This is driving me crazy, I just can't see how to do it. I want to express the cartesian unit vectors \hat{x}, \hat{y} and \hat{z} in terms of the spherical unit vectors \hat{r}, \hat{\theta} and \hat{\phi}. I have tried to do something similar in polar coordinates (just to make it a bit simpler...
Thanks a lot for the quick reply! What I meant was, what is the mathematical form of the operator \hat{B} that I introduced? For example, the form of the momentum operator \hat{p} in quamtum mechanics is - i \hbar \frac{d}{dx}, and the form of the laplace operator is:
\frac{d^2}{dx^2} +...
Can someone give me an example of a nonlinear operator? My textbooks always proves that some operator is a linear operator, but I don't think I really know what a nonlinear operator looks like.
One of my books defines an operator like \hat{B} \psi = \psi^2. I see that this is a nonlinear...
Hey!
Can someone tell me or just give a hint on how to show that:
\sum_n \frac{n^2 a^n}{n!}=a(1+a)e^a
when n goes to infinity? I know how to show that:
\sum_n \frac{n a^n}{n!}=a e^a
by using the facts that n/n! = 1/(n-1)! and a^n = a a^(n-1). But how can I prove the other one...
Hey!
I was wondering, is it merely a definition that
e^{ix}= cos(x) + i sin(x)
or is it actually important that it is the number e which is used as base for the exponential?
Thanks!
Can someone tell me how to show that the value of
x/[Sqrt(x^2+r^2)*r^2]
approaches 1/r^2 when x approaches infinity? Cant figure out how to show this analytically, but by plotting the function it is obvious.
Btw, how do I get latex graphics to work?? It doesn't really work when I...