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By Torr Kolen

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1). 27 ν = v 2 . 16 u = 0, v = 4xy u = cos x cosh y, v = sin x sinh y u = ±2−1/2 [(x2 + y 2 )1/2 + x]1/2 , v = ±2−1/2 [(x2 + y 2 )1/2 − x]1/2 , where the ± signs are chosen so that uv has the sign of y. u = ln(x2 + y 2 )1/2 , v = arc tan(y/x) [angle is in the quadrant of the point (x, y)]. 41 1 + iz − z 2 /2 − iz 3 /3! + z 4 /4! 42 z + z 3 /3! + z 5 /5!

28 Hyperbola: r2 cos(2θ + α) = K or (x2 − y 2 ) cos α − 2xy sin α = K K ln r = cosh(Kθ + C) Parabola: (x − y − C)2 = 4K 2 (x + y − K 2 ) m(¨ r − rθ˙2 ) + kr = 0, r2 θ˙ = const. m(¨ r − rθ˙2 ) + K/r2 = 0, r2 θ˙ = const. , z¨ + g = 0 1 ∂V 1 2 2¨ ˙ ˙2 r · m(r θ + 2rr˙ θ − r sin θ cos θ φ ) = − r ∂θ = Fθ = maθ 2 ¨ ˙ ˙ aθ = rθ + 2r˙ θ − r sin θ cos θ φ L = 21 ma2 θ˙2 − mga(1 − cos θ), aθ¨ + g sin θ = 0, θ measured from the downward direction. , = r2 θ˙ = const. 7   π −1 0 2  2 −1 π 0 Principal moments: I= (π − 1, π, π + 1); principal 15 15 0 0 π axes along the vectors: (1, 1, 0), (0, 0, 1), (1, −1, 0).

Y = bn sin nx cos nvt bn 6. 917ν10. 3. Some other examples of degeneracy: π 2 ¯h2 ; (nx , ny ) = (1, 8), (8, 1), (4, 7), (7, 4), giving En = 65 2ml2 similarly 22 + 92 = 62 + 72 = 85; 22 + 112 = 52 + 102 = 125, etc. 19 Ψ(r, θ, φ) = jl (βr)Pl (cos θ)e e , ¯h2 h2 , βa = zeros of jl , E = (zeros of jl )2 . 21 ψn (x) = e−α (x +y +z )/2 Hnx (αx)Hny (αy)Hnz (αz), α = mω/¯h, En = (nx + 12 + ny + 12 + nz + 12 )¯ hω = (n + 23 )¯ hω. (n + 2)(n + 1) , n = 0 to ∞. 21) are replaced by al r l −qR/a −q Pl (cos θ) = R2l+1 l r2 − 2(rR2 /a) cos θ + (R2 /a)2 Image charge -qR/a at(0, 0, R2 /a) LetK = line charge per unit length.

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An Experiment to Measure Relative Variations in the One-Way Velocity of light by Torr Kolen


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