What do you mean by the index for each value of f? I think what you're referring to is incorrect. Numerical integration techniques basically rely on one or another method for calculating the area under a curve, so you need some measure of "width."
In the simplest case, \int G(x) dx could be...
You're pretty much correct. The two spacetimes are metric spaces, in the sense that they are sets for which a distance between any two points is defined by some metric. There are several notions of equivalence between two metric spaces:
If there exists a continuous bijection between the two...
Just a couple of thoughts along those lines:
Probably doesn't need to be said, but just going to class AND paying attention goes a long way on its own.
When you get a little behind, there's a temptation to catch up by just learning "how to do" the things you missed, without making sure...
As far as I know, spiral galaxy structure is not cited as direct evidence for dark matter to begin with. In addition to several other areas of observation, however, DM provides a particularly nice solution for the galaxy rotation problem. For a generic spiral galaxy, assume we can derive the...
I'm assuming you want to get credit for the class, so first of all check with your school's policies regarding transfer credit and make sure they will count it. Rules about external/online class credit can vary from one school to another, so PF members won't be able to answer that for you...
No, that matrix is not correct. The cross product of the del operator \nabla and a vector function is just an alternate convention for denoting curl. You can why here: http://en.wikipedia.org/wiki/Del#Curl. This should also explain why divergence can be denoted: \nabla \cdot
So your matrix...
(b) is incorrect. The distance formula is d = v_{i}t+\frac{1}{2}at^{2} . Note that acceleration is negative in this case, and see if you can go from there.
The holes in the radiation shield of a microwave (or any effective radiation shield) need to be significantly smaller than the wavelength of the radiation. A typical kitchen microwave produces radiation on the order of ~5 inches.
Ignoring that a monochromatic radio wave is just "one color" anyway... the number of photons has to do with the intensity of the light, not the wavelength/frequency (see: Photoelectric effect). A "one photon" electromagnetic wave would be far, far too dim for the human eye to sense, even if we...
steveh721, a professor of mine (for a C and Fortran "scientific programming" class) recommended "Thinking in C++" by Bruce Eckel. https://www.amazon.com/Thinking-Introduction-Standard-One-2nd/dp/0139798099
Seeing as you have a lot of experience with C++, I'm just wondering what your thoughts...
Haha, alright. Think about finding a slope first rather than an angle first. What you want is \frac{dy}{dt} and \frac{dx}{dt} when it hits the water. The downward velocity and the horizontal velocity when it hits the water are components of its total velocity. Turn this into a triangle and...
Hint: 48.8 meters is a distance, 16.6 is a velocity, and you want the relevant x and y components to be in the same units. And it doesn't matter that the stone was thrown horizontally, you're concerned some that's happening at the time when it hits the water.