Thanks! Another way to see it.
One further detail:
I think we have been leaving out the absolute value sign.
\int \frac{1}{w} dw = \ln |w| + c
However wiki says this is true:
\frac{d}{dw} \ln(w) = \frac{1}{w}
Assuming that is true then using the fundamental theorem of calc we...
In the Tsiolkovsky rocket equation derivation there is a part that says:
\frac{dV}{dt} = -\upsilon_e \frac{1}{m} \frac{dm}{dt}
"Assuming v_e, is constant, this may be integrated to yield:"
\Delta V\ = v_e \ln \frac {m_0} {m_1}
How does this work? The differential is an operator...
exactly I am comfortable with where integrals exist. I am trying to explore where
\frac{dp}{dt} dt = dp
breaks down. It seems the only way for us to break this is to make
\frac{dp}{dt}
not exist. Do you think this is right or could it break some other way?
yep I know integrals are quite robust
does not [tex]\frac{dp}{dt}[\tex] on its own imply that p(t) is smooth, or that the derivative is continuous since otherwise the limit could have 2 values at a particular time t (one limit coming from the right (+) and one coming from the left(-))
quick question, I was watching an MITOCW physics lecture and I want to know where a principle breaks down.
\int^t_0 \frac{dp}{dt} dt = \int^{p(t)}_{p(0)} dp
how do I know such a thing is allowed? where does this break down? does it break down if p or t does not have property such as...
I would like to find out which functions retain the same structure when they are scaled. Particularly I am interested in projections.
For example, a parabola 3d space viewed at another angle can still be represented by at^2 + bt+c. A circle however can not (ellipse)
I am guessing conic...
Homework Statement
Is there a good way to do a fit. The fft looks simple:
I am trying to fit data from my experiment to the very nonlinear nested sine function given as equation 3 here:
http://www.physics.umd.edu/courses/Phys375/HillSpring10/Labs/Lab5Diffraction.pdf
Homework...
Where did the equations for the amplitude of the electric vectors come from? (the numerator and denominator of first post)?
Figured it out they, come from the fresnel equations.
Cipher made an error it should be 2cos(theta)sin(theta) = sin(2theta)
Oh one last question, if I wanted to use einstein summation notation here could I just leave off both sum symbols?
ie. is
\alpha_{ij}T_{ij} = 0
the same as
\sum_{i=1}^{n} \sum_{j=1}^{m} \alpha_{ij}T_{ij} = 0
using einstein summation notation?