What is Approximation: Definition and 761 Discussions

For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...

when: g'(2)=1 g'(3)= -2 msec=mtan g'(2.5)=(y2-y1)/(x2-x1) =(-2-1)/(3-2) =-3/1 =-3 I got this question wrong on a test, were was my mistake?

How do I find integrals like \int_{a}^{b} \left( x^2 + 1 \right)^2 \ dx . This one is easy, since I can just turn it into \int_{a}^{b} \left( x^4 + 2x^2 + 1 \right) \ dx . But what if it would say \int_{a}^{b} \left( x^2 + 1 \right)^{40} \ dx ? What technique should I use?

Is there any way to tell in general if an integral in the form of \int x^n*e^{x^m} dx where n and m are constants is solvable without approximation?

Can anybody explain to me what the Born approximation is?

Hello there. I'm currently dead beat on this problem, maybe because I'm not sure I quite understand what it's asking (I'm taking my upper level mechanics course in germany, and I don't have any books, and it's the second week, and I'm up at 4am with 2 problem sets due tomorrow, each half done...

I am a bit confused about taylor approximation. Taylor around x_0 yields f(x) = f(x_0) + f'(x_0)(x-x_0) + O(x^2) which is the tangent of f in x_0, where f'(x) = f'(x_0) + f''(x_0)(x-x_0) + O(x^2) which adds up to f(x) &=& f(x_0) + (f'(x_0) + f''(x_0)(x-x_0) +...

I'm doing a problem on Van-der Walls interaction and was told in the hint of the problem to use the approximation kT>>hw to simplify {-hw/(2kT)}-Ln[Exp[-hw/(kT)]-1] I have no idea how to apply this approximation to simpify the problem. Thanks

Does anyone know the basics of the local spin density approximation?

http://www.geocities.com/dr_physica/moa.zip is a delphi program showing how my method of approxim outperforms/beats the Newton's one while looking for sqrt(2) try the case A+B=2*sqrt(2) and see the magic!

I was wondering how Stirling's approximation x! ~ sqrt(2[pi]x)xxe-x was derived. Anyone know?