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  1. matt_crouch

    Maple Step by step solution in Maple

    Is it possible to get Maple to show me step by step how to solve a complex contour integral? f := (x,y,z,v) -> (x+I*x*cos(v)+I*y*sin(v))^(-2) int(f(x,y,z,v),v=0..2*Pi) assuming(x,real,y,real,z,real,v,real) But I would like to know how Maple solves this step by step. I tried using the tutor...
  2. matt_crouch

    Complex contour integrals

    So further from this, my original problem was to calculate the so called Whittaker contour integral so we start from $$f=\int_{0}^{2\pi} \frac{1}{(x+izcos(\vartheta)+iysin(\vartheta))^{2}}d\vartheta$$ This should give $$f=2\pi/r^(3)$$ could someone show me how? Essentially i changed from...
  3. matt_crouch

    Complex contour integrals

    Ok thanks for the replies everyone.... So the way I obtained the integral in the first place was to go from $$\vartheta \rightarrow \lambda,$$ by using $$\lambda = e^{i\vartheta}$$ So i guess the contour is an integration over the unit circle like Zinq said. Ok thanks for your comments
  4. matt_crouch

    Complex contour integrals

    I am trying to teach myself complex analysis . There seems to be multiple ways of achieving the same thing and I am unsure on which approach to take, I am also struggling to visualise the problem...Would someone show me step by step how to solve for example...
  5. matt_crouch

    Whittaker's solution and separable variables

    Would you show me how you solved the integral? I appear to be having some trouble
  6. matt_crouch

    Whittaker's solution and separable variables

    Pretty much, but where the solution to the Laplace equation is the addition of some function ##g(w)## and ##h(\tilde{w})## where ##\tilde{w}## is the complex conjugate of ##w##... The more I'm reading about it, it seems as if I need to look at twistor theory, global and local solutions etc...I...
  7. matt_crouch

    Whittaker's solution and separable variables

    So It is well known that the 2D solution to the Laplace equation can be obtained by changing to complex coordinates ##u=x+iy## and ##v=x-iy##. This can be extended to n dimensions as long as the complex coordinates chosen also solve the Laplace equation. For example in 3D...
  8. matt_crouch

    Integral inconsistency with variable change

    Ok thanks for your response. With regard to the first integral in the first post, you actually can show that they are both equivalent, ##\int (x+y)(dx+dy)=\int xdx +\int xdy+ \int ydx +\int ydy## from the relationship ##dw=dx+dy## we also get ##dx=dw-dy##, ##dy=dw-dx## if you substitute...
  9. matt_crouch

    Integral inconsistency with variable change

    However you can do the substitution for example in complex analysis where ##u=x+iy## and ##v=x-iy## with the differentials becoming ##du=dx+idy## and ##dv=dx-idy##, Is this substitution and hence the differentials valid because of the imaginary numbers? and hence when you integrate you can...
  10. matt_crouch

    Integral inconsistency with variable change

    so ## \int wdw = \frac{1}{2}w^{2} ## now if w=x+y, ## \int (x+y)(dx+dw)= \int xdx + \int ydx + \int xdy + \int ydy ## which can be evaluated and gives ##\int(x+y)(dx+dy)=\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2}## but ##\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2} \neq \frac{1}{2}w^{2}## can...
  11. matt_crouch

    Analytical integral

    can someone suggest a method to solve an integral of the form analytically? ##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##
  12. matt_crouch

    First order partial differential equation

    Hi sorry the subscript on the function was to represent a two 2d vector field. Is there a way to obtain an analytical solution if the function g is known?
  13. matt_crouch

    First order partial differential equation

    How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...
  14. matt_crouch

    Lorentz Transform of a radial & longitudinal dependent magnetic field

    Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution. Now initially i thought we would just use the standard LT...
  15. matt_crouch

    Starting a Phd in particle physics any advice?

    Accelerator physics text books Also one more question can anyone recommend any good text books for accelerator physics that they recommend
  16. matt_crouch

    Starting a Phd in particle physics any advice?

    Hi I wil be starting a PhD in particle/accelerator physics in September it's titled " beam dynamics and beam beam effects for Hilumi LHc and LHeC" Has anyone got any advice for me? It's a fully funded Phd at Manchester university Uk, but it's mainly based at the cockcroft institute. I'm...
  17. matt_crouch

    Calculate the spin wave dispersion relation for a ferromagnetic heisenberg model

    Homework Statement Calculate the spin wave dispersion relation Ek for the ferromagnetic heisenberg model with jtot = 1/2 Assume a 1d square lattice and interactions of strength J between nearest neighbours and zero elsewhere Homework Equations H|k> = [E0 +2jtot\sum J(r)(1-Exp(ik.r) ]...
  18. matt_crouch

    Nuclear physics problem

    you need to balance the reaction equation out so that you have basically 2(mhydrogen)= 1(mass of helium) + Δm then you can calculate the difference in mass. I can see one mistake and that is that you have used the value for C instead of C^2. Also note that the hydrogen has an initial kinetic...
  19. matt_crouch

    Is chemistry needed for astronomy/astrophysics

    im currently in the 3rd year of my degree doing a Mphys Physics with Astrophysics. I did do As Level chemistry and have done no more personally ive found that although some chemistry couldn't necessarily hurt its not essential. Further maths will help you more than chemistry will in my opinon
  20. matt_crouch

    Calculate the Change in entropy of the universe

    Homework Statement Calculate the changes in the entropy of the universe for a) A copper block of mass 0.5kg is dropped into a lake of 10 degrees with the block having a thermal capicity of 2J/K and a temperature of 100 degrees Homework Equations dS=dQ/T The Attempt at a...
  21. matt_crouch

    Fermions that can access 10 distinct energy states; Statistical Physics

    ok so because there is only 1 possible arrangement for u=1ev the statistical weight can be calculated used the equation above so Ω= 4!/4!(1)! Ω=1 so s=kln(1) then for the u=1.1 ev so the only possible state will be when 3/10 + 5/10 + 2/10 + 1/10 = 1.1 ev so again Ω=1 s=kln (1)
  22. matt_crouch

    Fermions that can access 10 distinct energy states; Statistical Physics

    Homework Statement Consider a system made of 4 quantum fermions that can access 10 distinct states respectively with energies: En=n/10 eV with n=1,2,3,4,5,6,7,8,9,10 1) Write the expression for the entropy when the particles can access all states with equal probability 2) Compute...
  23. matt_crouch

    Matlab code fitting a line to a histogram

    Im analyzing some data from a previous student im trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this...
  24. matt_crouch

    Plotting a best fit curve over a histogram

    Im analyzing some data from a previous student im trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this then...
  25. matt_crouch

    The Physics of Crumpled paper

    I am currently a 3rd year university student and the project i have been assigned is the the above title, and basically involves looking at statistal physics and its applications. My interests are all in astrophysics and cosmology i was wondering if there was any place for my interests in this...
  26. matt_crouch

    Calculate the electric field strength inside and outside a wire

    ahhh so i need to use the area of a cylinder? so 2(pi)rh +2(pi)r^2 ?
  27. matt_crouch

    Calculate the electric field strength inside and outside a wire

    ok so outside the conductor do i just use the E=q/4(pi)e0R^2 ?
  28. matt_crouch

    Calculate the electric field strength inside and outside a wire

    so since its a Gaussian surface do i calculate the line charge density by integrating lambda from R to infinity? then substitute that into the equation above?
  29. matt_crouch

    Calculate the electric field strength inside and outside a wire

    Homework Statement An infinitly long conducting cylinder of Radius R carries a unifom surface charge of (lambda per unit length) determine the electric field strength inside and outside the cylinder Homework Equations integral (E.ds)= q/e0 The Attempt at a Solution im not really sure what...
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