If z = f(x,y) and x = r \cos{v}, y = r\sin{v} the object is to show that d = \partial since it's easier to do on computer
Show that:
\frac{d^2 z}{dr^2} + \frac{1}{r} \frac{dz}{dr} + \frac{1}{r^2} \frac{d^2 z}{dv^2} = \frac{d^2 z}{dx^2} + \frac{d^2 z}{dy^2}
It's from Adams calculus, will...
I'm not 100% sure what this is in English so I'll try to describe it. Gives that:
A: x^2 < 16
B: -4 < x
C: -4 < x < 4
I'm supposed to put out every possibility for => and <=> between A,B and C. The key says that A => B, A <=> C and C => B. I can understand this, but isn't it true for...
Log is a multivalued function since e^x is a periodic function. Remember that Euler showed that
e^{ix} = \cos{x} + i\sin{x} and hence we have that e^x = e^{x + 2\pi i n and more general since a^x = e^{\ln{a} x} it's true that a^x is a periodic function.
Suppose we want to find
\int e^x \cos{x} \ dx
We know from e^{ix} = \cos{x} + i\sin{x} that the real part of e^{ix} equals \cos{x} . So suppose we want to find that integral, is it ok to study the real part of e^x \cdot e^{ix} ? In that case we get
\int e^x \cos{x} \ dx = \int...