Search results

  1. S

    Riemann Mapping theorem

    so i know what it is (i think lol) ... but what are its applications?
  2. S

    Scharwz lemma

    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...
  3. S

    Complex analysis - area inside a simple closed curve

    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
  4. S

    Openset / closedset / connected

    {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...
  5. S

    Complex analysis - maximum/modulus principle

    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...
  6. S

    Complex analysis - LFT

    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...
  7. S

    Complex analysis - argument principle

    (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...
  8. S

    Complex analysis - conformal maps -mapping

    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...
  9. S

    Harmonic functions - complex analysis

    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...
  10. S

    Linear fractional transformation

    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 ...
  11. S

    Log log ln

    my complex analysis book uses all three of them... although i know the difference between log and ln, I'm kinda clueless about Log ... any ideas?
  12. S

    Complex analysis - something really confusing

    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...
  13. S

    Limit of a series

    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...
  14. S

    Write a SIC program

    -------------------------------------------------------------------------------- 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...
  15. S

    Programs Double major in computer and electrical engineering

    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...
  16. S

    Suicidal/depressed for more than a year

    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 ...
  17. S

    News I'm writing a 12 page research paper on homelessness(USA)

    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...
  18. S

    I'm not sure if i should post it on the forums but

    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...
  19. S

    Understanding of wormholes

    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?
  20. S

    KE = p^2/(2m)

    refer to the title. I'm confused whether this eqn works in relativistic situations? thanks in advance
  21. S

    Back to the future - let's try it one more time

    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...
  22. S

    Back to the future - the movie

    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...
  23. S

    Objective reality

    your views on it?
  24. S

    Quantum mechanics

    Charges of +q and -q are separated by a distance L. What would be a typical energy of a virtual photon they exchange?
  25. S

    Paper on time travel

    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?
  26. S

    Help me find a couple of good articles

    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
  27. S

    Another quantum mechanics question

    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?
  28. S

    Quantum mechanics

    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