Recent content by DavidAlan

NVM. I suck. Google agrees. :(

You get |f(x)-f(y)||f(x)+f(y)| is always less than or equal to 2 epsilon. That is the condition you put on delta. You're trying to show that a delta exists that gives you continuity, not that there is an immutable value of delta that is special.

What's the largest that |f(x)+f(y)| can possibly be? Think about this for a second. If your expression |f(x)+f(y)| was bounded below, that would mean that |f(x)-f(y)||f(x)+f(y)| would always be LARGER than [itex]B\epsilon[\itex]. Once you have chosen epsilon, you are guaranteed that the...

Very good notes from an excellent professor of a class I took on PDEs: http://www.math.ucsb.edu/~grigoryan/124A/lecs/lec2.pdf Also, has anyone recommended Strauss' book? I printed all of these lecture notes in preparation of the final for the course. Reads much better than any book I've found.

You shouldn't do it this way. Remember, you specify epsilon and try to find some conditions to put on delta to guarantee continuity. Start with |f(x)-f(y)| is less than epsilon. Multiplying by |f(x)+f(y)| is the right thing to do, but the fact that |f(x)+f(y)| is arbitrarily small not a defect...

This is only a conventional point, but do not get in the habit of using partials in replace of "d" in integrals. That partial symbol is kind of sacred. It either refers to derivatives, Jacobian determinants, or the boundaries of open sets. When you use it in the sense of differentials, that be...

All good buddy. Why even mention diffeomorphisms? This be calculus, there be dragons there.

This might be looking too far into the future, but thinking of an integral as just being the area underneath a curve is very dangerous. It can be used to compute this sort of thing, but as far as I am concerned an integral is nothing more or less than the continuous analog of summation. When...

It is just notation. It means that the map entails some correspondence between sets. In English, the arrow points to the possible set of outputs of the map. If your map takes as its domain some set and "points" to the set of complex numbers, then your map is "complex valued," meaning that it...

I'm drunk, aren't you. For the love of god.

Sorry, posted wrong advice. Lol. This thing needs to be done in cylindrical coordinates I believe. Or as Joffan suggested, in standard Cartesian coordinates.

You just need to do some ugly integrals. What's the problem? If you want to do it using step functions or indicator functions or whatever your field calls them, write f(t) in terms of them, it doesn't really simplify the problem, just shows a preference in notation. For example, If...

A friend and I had an interesting thought and would like to know if it has any consequences. It is a well known fact that a time-varying electric field is non-conservative, it has a time-dependent Hamiltonian, blah, blah, blah, blah. I'll give this a standard treatment to set up the punchline...

I picked Griffiths up as a freshman as well, but only after I had taken a course on linear algebra and ODEs. You will need to supplement Griffiths with a good math methods text, I recommend Arfken. At your level some may recommend Boas, while it is also a good text, Arfken is much better. Arfken...

Compute it; it's very easy. Differentiate the probability amplitude and make substitutions using your "new" Schroedinger equation. The probability current will still be defined in the same manner.