a) The relationship would be,
|z| = \sqrt{x^2 + y^2} = r
&
|z^2| = |z|^2 = r^2
b) Okay, I got the series expanded by using the substitution.
f(z) = \frac{1}{2w^3} - \frac{1}{4w^2} + \frac{1}{8w} - ...
So, 1/8 is the residue.
c)
I found my mistake on part c)
I...
Homework Statement
a) Find the radius of convergence of the following complex series and the complex point, where the center of the disk of convergence is located:
\sum_{n=1}^{inf} 4^n (z-i-5)^{2n}
b) Find the Laurent series of the following function, f(z), about the singularity, z = 2, and...
Homework Statement
I did the lab and have to analyze the data to determine the quantized charge of an electron.
I have used the data to determine the 'total' charge on the observed drops using the following equation.Homework Equations
q = 3 ∏ r (E) η (Vup+Vdown)
Where r is the known radius of...
Homework Statement
For an ideal gas the slope of an isotherm is given by
(∂P/∂v) constant T = -P/v
and that of an isochore is
(∂P/∂T) constant v = P/T
Show that these relations give Pv = RT
Homework Equations
Pv = RT
The Attempt at a Solution
I have never worked with...
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