機器分析演習 - 神奈川大学理学部 · 11 375 4 fnj c anj c w 8bdgi8eh#tg { /.)" # l...
TRANSCRIPT
1
e
2
e
ex
ex =xn
n!n= 0
=1+ x +x 2
2!+x 3
3!+x 4
4!+x 5
5!+ ...
0! = 1
e =1+1
1!+1
2!+1
3!+1
4!+1
5!+ ...
3
Arcsin sin Arctan tan
Arcsin x <1
Arcsin(x) =(2n)!
4n (n!)2(2n +1)n= 0
x 2n+1
Arctan x 1
Arctan(x) =( 1)n
2n +1n= 0
x 2n+1
arcsin
sin(6) =1
2
Arcsin(1
2) =
6
(2n)! 0.52n+1
4n (n!)2(2n +1)n= 0
=6
sin( /2) = 1
4
tan(4) =1
Arctan(1) =4
( 1)n
2n +1n= 0
=4
Arctan
5
A Bk
k A [A]
d
dtA[ ]
A [A]
[A]
d[A]
dt= k •[A]
[A] t=0 [A] [A]0
ln[A]
[A]0
= k • t
[A] = [A]0 •exp k • t( ) exp x( ) = ex
6
d[A]
dt= lim
t 0
[A]
t
t [A] [A]
[A]
[A]0 A
[A] e
[A]
t= k •[A]
[A]
d
[A]0 k
t [A]
1/ 2 [A] [A]0 1/2 1/4 1/8
1/ 2 =1
kln2 t
s t t
7
A + B Ck
d
dtA[ ] [A]
d
dtB[ ] [B]
d
dtC[ ] [C]
A B
d[A]
dt= k •[A]•[B]
[A]0 = [B]0 [A] = [B]
d[A]
dt= k •[A]2
8
1
[A]
1
[A]0= k • t
[A]0 [B]0
ln[A]0[B]0
•[A]+ [B]0 [A]0
[A]
= ([B]0 [A]0)• k • t
[B]0 >> [A]0
[A]
t= k •[A]•[B]
B
[A]0 [B]0
k [A] [B]
k k
k
k
VLOOKUP
9
A Bk1
Ck2
d[A]dt
= k1 •[A]
d[B]
dt= k1 •[A] k2 •[B]
d[C]dt
= k2 •[B]
A Bk1
Ck2
k-1
d[A]dt
= k1 •[A]+ k 1 •[B]
d[B]
dt= k1 •[A] k 1 •[B] k2 •[B]
d[C]dt
= k2 •[B]
10
[A]0
k1 k2 [A] [B] [C]
[B]
[A] + [B] + [C]
k-1 A B
11
(1) A B
(2)
(3) p1
p1 • A
(4)
p-1
p 1 • A •B
(5) r1
r1 • A •B
(6) r-1
r 1 •B
[A]
t= p1 • A p 1 • A •B
[B]t
= r1 • A •B r 1 •B
12
0
0
13
cos(x) + x = 0
f (x) = cos(x) + x
f (x) f (x) = 0 x x
x0 x0, f (x0)( ) x x1 f (x)
x1 x0 x x
xx0x1x x2
f(x)
x0, f (x0)( ) y f (x0) = f (x0)• (x x0) y = 0
x1
x1 = x0f (x0)
f (x0)
14
xn +1 = xn
f (xn ) f (xn )
f (x) = cos(x) + x f (x) = sin(x) +1
xn+1 = xncos(xn ) + xnsin(xn ) +1
x0 x
2 x f(x) x x0
f(x)
0
x
15
f(x) g(x) f(x)+g(x)=0
x0
Newton x0
x0
16
(x, y)
y
( y)2
Excel
y=ax+b
slope a
intercept y b
rsq r2
3
17
Excel
y 0
18
Excel
y = aln x + b
y = a + bx + cx 2 + dx 3 + ...
y = axb
y = aebx
19
f (x) [x0, xn] f (x) dxx0
xn
[x0, xn] n x x1, x2, x3, …
x
x = x1 x0 = x2 x1 = x3 x2 = ...
xn x0 = n • x
f(x)
x0 x1 x2 x3 x4 xn
x
( f (x0) + f (x1)) x
2
i
20
( f (xi 1) + f (xi)) x
2
n
( f (xi 1) + f (xi)) x
2i=1
n
f (x) =1
1+ x 2[0, 1]
Arctan(x)
4
Excel
n
21
f (x) =1
1+ x 2[0, 1]
1
10
x=1 y=1
1 f (x) =1
1+ x 2
0 1 rand()
f (x) =1
1+ x 2
4
22
10 10
if