Recent content by matt_crouch

  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...
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