# Search results

1. ### 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. ### 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. ### 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. ### 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. ### Whittaker's solution and separable variables

Would you show me how you solved the integral? I appear to be having some trouble
6. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Lorentz Transform of a radial & longitudinal dependent magnetic field

Ok thanks.. I'll have a look through
15. ### 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...
16. ### Starting a Phd in particle physics any advice?

Accelerator physics textbooks Also one more question can anyone recommend any good textbooks for accelerator physics that they recommend
17. ### 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...
18. ### 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) ]...
19. ### 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...
20. ### 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 I've found that although some chemistry couldn't necessarily hurt its not essential. Further maths will help you more than chemistry will in my opinon
21. ### 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...
22. ### 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)
23. ### 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...
24. ### Matlab code fitting a line to a histogram

Im analyzing some data from a previous student I am 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...
25. ### Plotting a best fit curve over a histogram

Im analyzing some data from a previous student I am 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...
26. ### 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...
27. ### 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 ?
28. ### 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 ?
29. ### 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?
30. ### Calculate the electric field strength inside and outside a wire

Homework Statement An infinitly long conducting cylinder of Radius R carries a inform 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...
31. ### Multiple-choice problem why is this the answer?

try rearranging the equation to make |z| the subject
32. ### Derivative of (x^2+5x-1)/(x^2)

thats what i got... =]
33. ### Big Wheels or Small Wheels

im not sure but at first guess i would say they would remain the same.. although they would cover a greater distance per turn of the wheel it would need more energy to turn the wheel than for the smaller wheel. Not sure though that was just a quess =]
34. ### Doppler effect wavelength from car

actually i think i have the answer.. i used an equation that was stated in my textbook.. Wavelength behind = (vm+us)/Fs where Vm= velocity of sound in medium Us= velocity of source and it gets an answer of 0.6 m and wavelength infront = (vm-us)/Fs given an answer...
35. ### Doppler effect wavelength from car

well i can find the wavelength of the car but i think its only when its stationary I am not sure If Cs of the source is 30 m/s an the frequency is 600 hz then the wavelength is 0.05 m but I am not so sure where to go from there.. if i have Cs and Fs how do i find what the wavelength in front...
36. ### Doppler effect wavelength from car

Homework Statement A car is traveling at 30m/s in still air. the frequency of the siren on the car is 600hz. The velocity of sound in still air is 330 m/s. what is the wavelength of the sound waves a)directly in front of the car b)directly behind the car What is the frequency of the...
37. ### Work required to move capacitor plates

well since you know the force between the two plates Work is W=Integral (Fdr)
38. ### Describe geometrically the level surfaces of the functions

so you just square both sides so id get x2+y2+z2= C2 where C2 is just another constant is that right?
39. ### Describe geometrically the level surfaces of the functions

So the question is as titled i) f=(x^2 +y^2 +z^2) ^1/2 if I can figure out the method I can solve the other equations but I'm not really sure where to start I know that a function f(x,y,z) of a level surface well be constant so do I just find del f ?
40. ### Solar Power Requirments

it can be done. You need to know the average power used in a home over the year. Then calculate the amount of sun light that falls on the house. If you know the intensity of the sunlight over an area you can calculate the power. But you said that all energy can be traced back to the sun, I am...
41. ### Impulse and Momentum of an object

have you attempted the solution? how far have you got where are you stuck? you need to put the graph up as well i think =]
42. ### Newton’s law of universal gravitation

yes. but try and understand why. Write the equation out and look at how all the variables relate to each other an like compuchip said what happens to the force if you double one of the masses etc.

yes =]
44. ### Meaning of: Indicate magnitude & direction of all vectors

ahhh i see where u have made the mistake remember that when the ball is thrown upwards it is still under the influence of gravity so you can't use v=s/t because that assumes that the object isn't accelerating and it is in fact decelerating, gravity is slowing the ball down.For part C its the...
45. ### Meaning of: Indicate magnitude & direction of all vectors

Velocity and displacement for example are vectors. Vectors have both magnitude and direction opposed to scalers which have purely magnitude. You basically have got to say which direction it is acting in so for example if a ball is thrown upwards the force of gravity acts in the opposite...
46. ### Matter/Antimatter annhialation

just out of interest if matter can be converted to energy can energy be converted to matter. I was asked this and i think the answer is yes but i can't think of a situation where it would happen
47. ### Eigenvalues homework problem

ok i got to the cubic polynomial and just want to check that i have the right polynomial im rubbish with latex so let x = lambda x3+6x2+20x=0 i then simplified to get -x(x2-6x-20)=0
48. ### Eigenvalues homework problem

Homework Statement Show that lambda = 1 is an eigenvalue of the matrix 2,-1, 6 3,-3, 27 1,-1, 7 and find the eigenvalues and the corresponding eigenvectors Homework Equations The Attempt at a Solution I don't understand how to actually get eigenvalues and...
49. ### Finding speed

use the conservation of momentum
50. ### Easy question has me confused (Inclined plane)

hmmm not sure then. ill have another look we both must be missing something obvious :/