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### GreenPDE

Course: PHY 318, Spring 2009
School: Duke
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Word Count: 332

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318 Physics Electromagnetism Greens Function for the Poisson Equation 1. The nonhomogeneous problem for the Poisson Equation 2 R.G. Palmer 4/13/09 (x) = (x)/0 in a domain V Closed boundary conditions on (x) at the surface S 2. The Greens function G(x, x ) 2 G(x, x ) = 4 (x x ) 3. The magic rule (x) = 1 40 G(x , x)(x ) d3x V 1 4 (x ) S G (x , x) G(x , x) (x ) da n n 4. Homogeneous boundary conditions...

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318 Physics Electromagnetism Greens Function for the Poisson Equation 1. The nonhomogeneous problem for the Poisson Equation 2 R.G. Palmer 4/13/09 (x) = (x)/0 in a domain V Closed boundary conditions on (x) at the surface S 2. The Greens function G(x, x ) 2 G(x, x ) = 4 (x x ) 3. The magic rule (x) = 1 40 G(x , x)(x ) d3x V 1 4 (x ) S G (x , x) G(x , x) (x ) da n n 4. Homogeneous boundary conditions for G(x, x ) We can choose homogeneous boundary conditions for G(x, x ) on S . Then G(x, x ) = G(x , x) Often we use the Dirichlet BCs (G(x, x ) = 0 for x on S ), giving (x) = 1 40 GD (x, x )(x ) d3x V 1 4 (x ) S GD (x, x )da n (x )da n (Dirichlet Greens Fn) or the Neumann BCs (G(x, x )/n = for 4/S x on S ), giving (x) = S + 1 40 GN (x, x )(x ) d3x + V 1 4 GN (x, x ) S (Neumann Greens Fn) 5. Techniques for constructing Greens function a. Method of images. [J2.6] b. Fundamental solution (1/|x x |) + solutions for Laplaces equation. [J1.10] c. Eigenfunction expansions for two dimensions and using the matching method for the third. [J3.9, J3.11] d. Eigenfunction expansions for three dimensions (see below). ...

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Exam 1 Grades16 12 8 4 0FD-D D+ C-C C+ B-BB+ A-ALight = Electromagnetic WaveOscillations of the Electromagnetic (E-M) FieldAt one moment in time, the electric field E varies with position: E = Wavelength Amplitudex EP P = Perio
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Please pick up a FERPA release form! Return it down front at the end of the class.Stars: Absorption LinesNebulae: Emission linesSun's Atmosphere (size exaggerated)Electrons in atoms can only be in specified energy levels or orbitals. Analogy
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How fast?Red light : 6,000 Green light : 5,000 obs orig z= = or i g 1000 1 z= = 6000 6 v 1 = c 6 1 v= c 6Redshift or Blueshift?What will you see?A B C DRedshift Neither Blueshift Not Enough InfoGetting Closer (Approaching)Getting
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Today : evidence for Dark matter Tutorial : Gravity and OrbitsNormal MatterDark Matter Dark EnergyConstituents of the UniverseKeplerian OrbitsVenus Earth Marsvv (km/s)Jupiter1 rSaturnUranusr (AU)Image : Roy, physcs/0007025Ro
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Normal Matter : stuff made of protons, neutrons, and electrons (i.e. us, stars, hot X-ray gas in clusters, etc.) is the only stuff that emits or absorbs light. is only ~5% of the total energy density of the Universe Dark Matter : holds galaxies a
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