f(x) = e x2 25 d f(x) 0 x d2 dx f(x) 0 x dx2 f(x) (1 + ax 2 ) 2 lim x 0 x 4 a 3 2 a g(x) = 1 + ax 2 f(x) g(x) 1/2 f(x)dx n n A f(x) = Ax (x R
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1 29 ( )
2 f(x) = e x2 25 d f(x) 0 x d2 dx f(x) 0 x dx2 f(x) (1 + ax 2 ) 2 lim x 0 x 4 a 3 2 a g(x) = 1 + ax 2 f(x) g(x) 1/2 f(x)dx n n A f(x) = Ax (x R n ) 25 A 2 = A A 2 A 2 = A t A = A A t A A 3 n = 2 A 2 = O A f Ker(f) m(f) 1
3 n (n > 2) x 1, x 2,, x n G A A k (i, j) (A k ) ij 3 G G 50 G A x l x l 3 A = G A 3 (A) ij (A 2 ) ij 0 i, j G 2
4 4 C C i, N i, P i, S i C = 10 i N i FUN 1 FUN 2 FUN 3 FUN 4 P i S i C ( ) C (j = 1, 2,, C) j (V 4 j ) 4 4 (V i j ) j = 1, 2,, 10 i = 1,, j Vj 1 0 Vj 2 0 Vj 3 0 Vj 4 0 3
5 2 3 4 i = 1 N 1 j(= 1, 2,,C) (V 1 j ) L j ( ) V 1 j 0 L j i = 2 N 1 N 2 j(= 1, 2,, C) (V 2 j ) L j 2 i = 3 N 1 N 2 N 3 j(= 1, 2,, C) (V 3 j ) L j 2 i = 4 N 1 N 2 N 3 N 4 j(= 1, 2,, C) (V 4 j ) L j 2 C 2 Vj i = Vj i 1 j j S i 0 P i + V i j S i j Vj i V j i P i + Vj S i i L j L j Si N i V k 0 = 0 (k = 1,, 4) 4
6 T1 10 T2 T1 T
7 29 ( ) CT
8 f(x) = e x2 25 d f(x) 0 x d2 dx f(x) 0 x dx2 f(x) (1 + ax 2 ) 2 lim x 0 x 4 a 3 2 a g(x) = 1 + ax 2 f(x) g(x) 1/2 f(x)dx n n A f(x) = Ax (x R n ) 25 A 2 = A A 2 A 2 = A t A = A A t A A 3 n = 2 A 2 = O A f Ker(f) m(f) 1
9 n (n > 2) x 1, x 2,, x n G A A k (i, j) (A k ) ij 3 G G 50 G A x l x l 3 A = G A 3 (A) ij (A 2 ) ij 0 i, j G 2
10 4 C C i, N i, P i, S i C = 10 i N i FUN 1 FUN 2 FUN 3 FUN 4 P i S i C ( ) C (j = 1, 2,, C) j (V 4 j ) 4 4 (V i j ) j = 1, 2,, 10 i = 1,, j Vj 1 0 Vj 2 0 Vj 3 0 Vj 4 0 3
11 2 3 4 i = 1 N 1 j(= 1, 2,,C) (V 1 j ) L j ( ) V 1 j 0 L j i = 2 N 1 N 2 j(= 1, 2,, C) (V 2 j ) L j 2 i = 3 N 1 N 2 N 3 j(= 1, 2,, C) (V 3 j ) L j 2 i = 4 N 1 N 2 N 3 N 4 j(= 1, 2,, C) (V 4 j ) L j 2 C 2 Vj i = Vj i 1 j j S i 0 P i + V i j S i j Vj i V j i P i + Vj S i i L j L j Si N i V k 0 = 0 (k = 1,, 4) 4
12 T1 10 T2 T1 T
13 29 ( )
14
15 50 Atkinson Shiffrin (1968) Craik Lockhart (1972) 250 Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. n K. W. Spence & J. T. Spence (Eds.), The psychology of learning and motivation, Vol. 2. New York: Academic Press, pp Craik, F.. M., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. Journal of Verbal Learning and Verbal Behavior, 11, pp
16 pp
17 4 C C i, N i, P i, S i C = 10 i N i FUN 1 FUN 2 FUN 3 FUN 4 P i S i C ( ) C (j = 1, 2,, C) j (V 4 j ) 4 4 (V i j ) j = 1, 2,, 10 i = 1,, j Vj 1 0 Vj 2 0 Vj 3 0 Vj 4 0 4
18 2 3 4 i = 1 N 1 j(= 1, 2,,C) (V 1 j ) L j ( ) V 1 j 0 L j i = 2 N 1 N 2 j(= 1, 2,, C) (V 2 j ) L j 2 i = 3 N 1 N 2 N 3 j(= 1, 2,, C) (V 3 j ) L j 2 i = 4 N 1 N 2 N 3 N 4 j(= 1, 2,, C) (V 4 j ) L j 2 C 2 Vj i = Vj i 1 j j S i 0 P i + V i j S i j Vj i V j i P i + Vj S i i L j L j Si N i V k 0 = 0 (k = 1,, 4) 5
19 29 ( )
20 f(x) = e x2 25 d f(x) 0 x d2 dx f(x) 0 x dx2 f(x) (1 + ax 2 ) 2 lim x 0 x 4 a 3 2 a g(x) = 1 + ax 2 f(x) g(x) 1/2 f(x)dx n n A f(x) = Ax (x R n ) 25 A 2 = A A 2 A 2 = A t A = A A t A A 3 n = 2 A 2 = O A f Ker(f) m(f) 1
21 n (n > 2) x 1, x 2,, x n G A A k (i, j) (A k ) ij 3 G G 50 G A x l x l 3 A = G A 3 (A) ij (A 2 ) ij 0 i, j G 2
22 D z = x + iy w(z) = u(x, y) + iv(x, y) w u, v Cauchy-Riemann u x = v y u y = v x u, v, x, y R, i = 1 50 u, v 2 u x u y 2 = 0 2 v x v y 2 = 0 2 x = r cos θ, y = r sin θ Cauchy-Riemann u r = 1 r v θ v r = 1 r u θ 3 w u u = x 3 + axy 2 a w a v(1, 1) = 0 w v 3
23 4 C C i, N i, P i, S i C = 10 i N i FUN 1 FUN 2 FUN 3 FUN 4 P i S i C ( ) C (j = 1, 2,, C) j (V 4 j ) 4 4 (V i j ) j = 1, 2,, 10 i = 1,, j Vj 1 0 Vj 2 0 Vj 3 0 Vj 4 0 4
24 2 3 4 i = 1 N 1 j(= 1, 2,,C) (V 1 j ) L j ( ) V 1 j 0 L j i = 2 N 1 N 2 j(= 1, 2,, C) (V 2 j ) L j 2 i = 3 N 1 N 2 N 3 j(= 1, 2,, C) (V 3 j ) L j 2 i = 4 N 1 N 2 N 3 N 4 j(= 1, 2,, C) (V 4 j ) L j 2 C 2 Vj i = Vj i 1 j j S i 0 P i + V i j S i j Vj i V j i P i + Vj S i i L j L j Si N i V k 0 = 0 (k = 1,, 4) 5
25 29 ( )
26 f(x) = e x2 25 d f(x) 0 x d2 dx f(x) 0 x dx2 f(x) (1 + ax 2 ) 2 lim x 0 x 4 a 3 2 a g(x) = 1 + ax 2 f(x) g(x) 1/2 f(x)dx n n A f(x) = Ax (x R n ) 25 A 2 = A A 2 A 2 = A t A = A A t A A 3 n = 2 A 2 = O A f Ker(f) m(f) 1
27 n (n > 2) x 1, x 2,, x n G A A k (i, j) (A k ) ij 3 G G 50 G A x l x l 3 A = G A 3 (A) ij (A 2 ) ij 0 i, j G 2
28
29 4 C C i, N i, P i, S i C = 10 i N i FUN 1 FUN 2 FUN 3 FUN 4 P i S i C ( ) C (j = 1, 2,, C) j (V 4 j ) 4 4 (V i j ) j = 1, 2,, 10 i = 1,, j Vj 1 0 Vj 2 0 Vj 3 0 Vj 4 0 4
30 2 3 4 i = 1 N 1 j(= 1, 2,,C) (V 1 j ) L j ( ) V 1 j 0 L j i = 2 N 1 N 2 j(= 1, 2,, C) (V 2 j ) L j 2 i = 3 N 1 N 2 N 3 j(= 1, 2,, C) (V 3 j ) L j 2 i = 4 N 1 N 2 N 3 N 4 j(= 1, 2,, C) (V 4 j ) L j 2 C 2 Vj i = Vj i 1 j j S i 0 P i + V i j S i j Vj i V j i P i + Vj S i i L j L j Si N i V k 0 = 0 (k = 1,, 4) 5
36 3 D f(z) D z f(z) z Taylor z D C f(z) z C C f (z) C f(z) f (z) f(z) D C D D z C C 3.: f(z) 3. f (z) f 2 (z) D D D D D f (z) f 2 (z) D D f (z) f 2 (
3 3. D f(z) D D D D D D D D f(z) D f (z) f (z) f(z) D (i) (ii) (iii) f(z) = ( ) n z n = z + z 2 z 3 + n= z < z < z > f (z) = e t(+z) dt Re z> Re z> [ ] f (z) = e t(+z) = (Rez> ) +z +z t= z < f(z) Taylor
More information() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
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1 1.1 [] f(x) f(x + T ) = f(x) (1.1), f(x), T f(x) x T 1 ) f(x) = sin x, T = 2 sin (x + 2) = sin x, sin x 2 [] n f(x + nt ) = f(x) (1.2) T [] 2 f(x) g(x) T, h 1 (x) = af(x)+ bg(x) 2 h 2 (x) = f(x)g(x)
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..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................
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f(x) f(z) z = x + i f(z). x f(x) + R f(x)dx = lim f(x)dx. R + f(x)dx = = lim R f(x)dx + f(x)dx f(x)dx + lim R R f(x)dx Im z R Re z.: +R. R f(z) = R f(x)dx + f(z) 3 4 R f(x)dx = f(z) f(z) R f(z) = lim R
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