so the way book states it, for the sc. lemma to work, |f(z)| has to be less than or equal to 1 and and z has to be less than 1. However, the book seems to use the lemma in some problems even if one of the conditions is not satisfied ... any help with gretaly appreciated
also ...if you could...
Let C be a simple closed curve. Show that the area enclosed by C is given by 1/2i * integral of conjugate of z over the curve C with respect to z.
the hint says: use polar coordinates
i can prove it for a circle, but i am not sure how to extend it to prove it for any given closed curve
{z^2: z = x+iy, x>0, y>0}
i am a lil confused about the notation to represent the set ...
i'm used to seeing {z: z = x+iy, x>0, y>0}
but what effect does squaring z have?
i thought the set was open simply because x>0 and y>0 ... but apprently i was wrong ... (or maybe not?) ... i...
Suppose that f is analytic on a domain D, which contains a simple closed curve lambda and the inside of lambda. If |f| is constant on lambda, then either f is constant or f has a zero inside lambda ...
i am supposed to use maximum/modulus principle to prove it ...
here is my take:
if f...
Verify that the linear fractional transformation
T(z) = (z2 - z1) / (z - z1)
maps z1 to infinity, z2 to 1 and infinity to zero.
^^^ so for problems like these, do I just plug in z1, z2 and infinity in the eqn given for T(z) and see what value they give?
in this case, do i assume 1/ 0 is...
(changes in arg h (z) as z traverses lambda)/(2pi) =
# of zeroes of h inside lambda +
# of holes of h inside lambda
now the doubt i have is what happens when the change i get in h (z) is say 9 pi/2 .... because then i would have a 2.5 on left side of the eqn ... so do i round it up and...
find a one-to-one analytic function that maps the domain {} to upper half plane etc ...
for questions like these, do we just have to be blessed with good intuition or there are actually sound mathematical ways to come up with one-to-one analytic functions that satisfy the given requirement...
so .. if f (z) = u + iv is analytic on D, then u and v are harmonic on D...
now ...
if f (z) never vanishes on the domain ...
then show log |f (z)| is harmonic on the domain ...
Recall: harmonic means second partial derivative of f with respect to x + second partial derivative of f with...
sooo ...
i am kind of clueless about how to determine a linear fractional transformation for a circle that maps on to a line or vice versa ...
like i do *kinda* get how to map a circle on to a circle ... or a line on to a line ...
I think I have misunderstood one of the theorems in complex analysis
(k reperesents the order of the derivative)
Theorem: Suppose f is analytic on a domain D and, further, at some point z0 subset of D, f (k) (z0) = 0. Then f(z) = 0 for all z subset of D ...
Is the theorem basically...
so there is a power series
S 4^n z^(3n)
and upper limit being infinity and lower limit being 0. (S means sigma)
then my book says, ak = 4^ (k/3) if k = 0, 3, 6...
and ak equals 0 otherwise.
i dont get how they came up for the value of ak
i might be missing something silly ...
any...
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Write a SIC program whose inputs are
two blocks of integers, BLK1 and BLK2 and whose output is a third
block of integer, BLK3. Each of these blocks contains 50
integers. Your program will take the integers in...
I'm majoring in computer engineering ...
so I was wondering if I should double major by majoring in electrical engineering as well?
I think what I'm trying to ask is ...
1) What's the importance of this particular double major in terms of jobs?
2)How does it look on grad school...
so as you guys already know, i'm mentally ill ... I have been suicidal/depressed for more than a year (and i'm still alive wow!)
I'm also epileptic ... and I have several physical problems as well, but I would rather not discuss them on here
but hey i'm not about to die or anything ...
here is my thesis statement :
In a rich nation like the USA, homelessness has deeper causes than poverty: mismanagement in housing programs, deinstitutionalization of mentally ill people and foster care.
OR
Poverty is the fundamental reason for the circumstantial homelessness from the...
do you guys know of a forum where i can post my all study related questions, not just the ones based on physics?
being mentally ill, i hardly have courage to finish or even start an assignment especially a paper until someone guides me. Sometimes, the person does not even need to do anything...
from my understanding of wormholes, you can use a wormhole to build a time machine to go back in past.
However, i think you cant go back in time before the time machine was built... right? or is there a way around?
so the discussion on the movie last time didnt go too well, coz i focused on scienctific concepts rather than the philosophy ... so i decided to make another thread
1)does back to the future at any point tell that marty actually slipped in parallel reality? or it doesnt become clear...
sorry, I dont think I'm posting this thread in the right section, but then I'm not sure which section this thread belongs to
I would really like to discuss the movie "Back to the Future (1985)" coz I just saw it ...
btw something I couldnt understand was the significance of 88 miles per...
do you think it's a good idea to write a 10 page research paper on time travel?
if not on time travel, could you possibly suggest something in modern physics that i can easily write a research paper on?
can you please help me find a good article on all that weird stuff in modern physics? the article can be specific or general ... it doesnt really matter as long as it pertains to modern physics
The equations for R and T in the E > U0 barrier are essentially the same as for light passing through a transparent film. It is possible to fabricate a thin film that reflects no light? Is it possible to fabricate one that transmits no light?
Why or why not?
if you know the wave ...
how do you determine the reflected and transmitted waves?
the book tells you to enforce the required continuity conditions to obtain their (possibly complex) amplitudes