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Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e
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Fortran90/95 2. (p 74) f g h x y z f x h x = f x + g x h y = f y + g y h z = f z + g z f x f y f y f h = f + g Fortran 1 3 a b c c(1) = a(1) + b(1) c(
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2 K = f (x) K[[x]] = r f (x) r D = D (0, r) a D f (x) a D Figure X d : X X R 0 d(x, z) max{d(x, y), d(y, z)} x, y, z X (X, d) clopen 1.1. (X,
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Donaldson Seiberg-Witten [GNY] f U U C 1 f(z)dz = Res f(a) 2πi C a U U α = f(z)dz dα = 0 U f U U P 1 α 0 a P 1 Res a α = 0. P 1 Donaldson Seib
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I = [a, b] R γ : I C γ(a) = γ(b) z C \ γ(i) 1(4) γ z winding number index Ind γ (z) = φ(b, z) φ(a, z) φ 1(1) (i)(ii) 1 1 c C \ {0} B(c; c ) L c z B(c;
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.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,
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I.2 z x, y i z = x + iy. x, y z (real part), (imaginary part), x = Re(z), y = Im(z). () i. (2) 2 z = x + iy, z 2 = x 2 + iy 2,, z ± z 2 = (x ± x 2 ) +
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No. No. 4 No f(z) z = z z n n sin x x dx = π, π n sin(mπ/n) x m + x n dx = m, n m < n e z, sin z, cos z, log z, z α 4 4 9
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3 filename=quantum-3dim110705a.tex ,2 [1],[2],[3] [3] U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h
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7. y fx, z gy z gfx dz dx dz dy dy dx. g f a g bf a b fa 7., chain ule Ω, D R n, R m a Ω, f : Ω R m, g : D R l, fω D, b fa, f a g b g f a g f a g bf a
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R 3 4 a 1 = 2 2 4, a 2 = α 1, a 3 = 1 1 α, b=., α., a 1, a 2, a 3 1, 2, 3 x 3 A = [a 1 a 2 a 3 ] 1 Ax=b, x= y z, rank A, rank [A b]. 4α 2 (1) α
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(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z
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