: α α α f B - 3: Barle 4: α, β, Θ, θ α β θ Θ
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1 : Bragg-Brenano x 1 Bragg-Brenano focal geomer 1 Bragg-Brenano α α 1 1 α < α < f B α 3 α α Barle 1. 4 α β θ 1
2 : α α α f B - 3: Barle 4: α, β, Θ, θ α β θ Θ
3 Θ θ θ Θ α, β θ Θ 5 a, a, a, b, b, b a a a b b b 5: a, a, a, b, b, b R a b R a R/ cos α 3 b R/ cos β 4 a R an α 5 b R an β 6 a b θ a b a b cos θ R cos θ cos α cos β 7 a b a a b b a b a b a b cos Θ a b R cos Θ an α an β 8 a b, b a, a b a b cos θ cos Θ an α an β 9 cos α cos β cos θ cos Θ cos α cos β sin α sin β 1 3
4 θ Θ α β.3 Θ θ Θ θ 1 Θ arccos cos θ an α an β θ 11 cos α cos β α β Talor α β α β 1 α α αβ 1 α β β β 1 α β, / α, / β, / α, / α β, / β α β cosθ cos Θ cos α cos β sin α sin β 13 cosθ cos Θ α sinθ cos Θ sin α cos β cos α sin β 16 α α β sin Θ 17 α / α 13 β sinθ cos Θ cos α sin β sin α cos β 18 β α β / β 4
5 16 α sinθ cosθ cos Θ cos α cos β sin α sin β 19 α α α β / α α sin Θ cos Θ / α co Θ 18 β / β co Θ 16 β α β sinθ cosθ cos Θ sin α sin β cos α cos β 1 α β α β / α / β sin Θ 1 α β / α β 1/ sin Θ α β Talor α β an Θ αβ sin Θ 3.4 w A z w A z δz f B αf B βdα dβ δ z α β an Θ αβ f B αf B βdα dβ 4 sin Θ x α β 4 an Θ 1 an Θ 1 an Θ an Θ 1 1 sin Θ 1 sin Θ cos Θ 1 cos Θ an Θ 1 α β an Θ αβ sin Θ α β 1 αβ1 4 α β α β
6 α x, β x x α β, α β x fα, βdαdβ fα, βdαdβ β α x β dα dx α x f x β, βdx dβ f x β, βdβ dx 9 x β x / dβ d/ β f f f x x, x d dx x, x d dx 4 9 w A z δ z α β an Θ αβ sin Θ δ z 1 x x, x dx d 3 f B αf B βdα dβ x x f B f B dx d Barle ϕ 1 1 ϕ < ϕ < f B ϕ 6 31 : x x : 31 w BB z 1 δ z x x x 1 1 dx d
7 x - - 6: Barle BB Barle w BB z δ z x x x 1 1 dx d 34 x x w BB z 4 δ z x 1 x x 1 dx d 35 1/ z z δ w BB z; w BB z; w BB z; 1/ 36 < 1 1 < < 1 35 z / x / u z / u x / x z u/ / x z u / xdx du dx du/x du/ z u x u z / z / / w BB z 4 z / ] / 1 1 z u z / 1 1 ] z u δ u du d 37 z u 7
8 δ- a < b b a fuδudu b a fuδ udu { f a < < b 37 z < < z < z < z u > z < z < 1 < z 1 < z / 4 z z - / 1/ - / z / 1/ Region V Region IV Region III z - / Region II - / Region I 7: 37, z z < / Region I < z Region V w BB z / z z 3 Region II, III, IV 8
9 .4.1 z < z < 7 Region IV 1 z < z z 1 ] z w BBz z z z 1 z d 1 ] ] 1 1 z ] z d z 1 z 1 z ] 1 d z 1 d z d z 44 x ± a dx 1 x x ± a ± a ln x ] x ± a dx ln x x ± a x ± a V 1 4 zd d 1 z d z 47 9
10 V 1 z z ln 1 z ] z ln z 1 4 z 1 z1 ln z 1 ] z 4 1 z1 ln z 48 V 4 w BBz V 1 V 49 u z 1 u u ln ] u ln ] 5 51 V 1 ] u u u 53 1 u 1 u u 1 u 54 V 1 1 u
11 < u V 1 u 56 4 w BB V 1 V 1 1 u 1 1 u 1 u 1 1 u 57 z1 1 u u u1 1 u1 u1 ] 1 1 u 1 1 u1 1 1 u ] < z < 1 < u < 1 1 < u1 < 1 < 1 u1 < 1 < 1 u1 < 1 1 u u 1 < 1 u1 < 1 < 1 1 u1 < 1 1 u u1 1 1 u ] 1 u u
12 ] u u u1 3 1 u1 1 1 u1 ] 3 1 u1 1 1 u1 1 u 3 1 u1 1 6 u1 1 u 3 1 u1 V 1 1 u1 V w BB V 1 V 1 u 3 1 u1 1 u1 1 1 u ln 1 u 1 1 u u u u u1 ln u 1 1 u1 65 u z u 1 4 w BB 1 1 ln
13 .4. / z 1 /4 / z 1 /4 8 7 Region II 1 z w BBz ] ] 1 1 z 1 1 z 1 1 ] z d z 1 z z 1 z ] 1 d z 1 1 z d z d 1 z 1 d z d z 68 xdx x ± a x ± a 69 V 1 4 z z ln z 1 z ] z ln z 1 4 z z z1 1 z ] ln z z1 ] ln z z 7 4 w BBz V 1 V 71 u z 7 13
14 V u u z u 74 u 75 V 1 1 u 76 1 u u1 1 < 1 1 u 1 1 u 1 1 u1 1 < u1 1 u u u 1 u 77 < 1 1 u u u u1 1 u1 3 1 { 1 1 u1 ]} 3 1 u1 1 u u1 3 1 u1 1 1 u
15 1 V 1 1 u 3 1 u1 1 1 u u1 1 4 w BBz V 1 V 1 u 3 1 u1 1 1 u u1 u 1 1 u 3 1 u1 1 1 u1 1 1 u 79 ln 1 1 u1 u1 8 z / u 1/ 1 / / 4 w BB / / ln 1 1 1/ 1 1/ ln 1 1/ 1 / /4 < z < < Region III, z u 15
16 3 3 z 1 u < < 1 < < 3 4 w BBz V 1 V 3 V 3 V 83 V 1 V V 3 V 3 3 u u u 1 u V u u ln u 1 84 ] u u V u u 1 1 u u u V u u 86 16
17 u 1 u V u 1 1 u u u u 3 1 u1 V 1 1 u u V 1 1 u 4 w BBz V 1 V 3 V 3 V 1 u 3 1 u1 1 u u 1 1 u1 1 u u u 1 1 u u u u 3 1 u1 1 u u1 u u u ln u 1 1 u
18 1 1 u 1 u 3 1 u1 1 u u1 u1 ln 1 1 u1 u u1 u z, an θ u z 89 u < 1 Region I: z / w BB z 9 Region II: / < z 1 /4 1 u 3 1 u1 4 w BBz 1 1 u u1 91 u1 Region III: 1 /4 < z < 1 u 3 1 u1 4 w BBz 1 u u1 u1 ln 1 1 u1 u u1 u1 Region IV: < z 1 u 3 1 u1 4 w BBz 1 u1 Region V: z 1 1 u 9 ln 1 1 u1 u1 93 w BB z 94 > 1 w BB z; w BB z; 1/ 18
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1 c Koichi Suga, ISBN
c Koichi Suga, 4 4 6 5 ISBN 978-4-64-6445- 4 ( ) x(t) t u(t) t {u(t)} {x(t)} () T, (), (3), (4) max J = {u(t)} V (x, u)dt ẋ = f(x, u) x() = x x(t ) = x T (), x, u, t ẋ x t u u ẋ = f(x, u) x(t ) = x T x(t
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145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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2000年度『数学展望 I』講義録
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漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
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『共形場理論』
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.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
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κ κ κ κ κ κ μ μ β β β γ α α β β γ α β α α α γ α β β γ μ β β μ μ α ββ β β β β β β β β β β β β β β β β β β γ β μ μ μ μμ μ μ μ μ β β μ μ μ μ μ μ μ μ μ μ μ μ μ μ β
経済数学演習問題 2018 年 5 月 29 日 I a, b, c R n に対して a + b + c 2 = a 2 + b 2 + c 2 + 2( a, b) + 2( b, c) + 2( a, c) が成立することを示しましょう.( 線型代数学 教科書 13 ページ 演習 1.17)
経済数学演習問題 8 年 月 9 日 I a, b, c R n に対して a + b + c a + b + c + a, b + b, c + a, c が成立することを示しましょう. 線型代数学 教科書 ページ 演習.7 II a R n がすべての x R n に対して垂直, すなわち a, x x R n が成立するとします. このとき a となることを示しましょう. 線型代数学 教科書
1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2
θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =
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1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1
sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V
1. z dr er r sinθ dϕ eϕ r dθ eθ dr θ dr dθ r x 0 ϕ r sinθ dϕ r sinθ dϕ y dr dr er r dθ eθ r sinθ dϕ eϕ 2. (r, θ, φ) 2 dr 1 h r dr 1 e r h θ dθ 1 e θ h
IB IIA 1 1 r, θ, φ 1 (r, θ, φ)., r, θ, φ 0 r