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1 bit 8, 6, 3 bit byte = 8 bit, char CBYTEFORTRAN) 055, -87 word = 6 bit int (C) INTEGER (FORTRAN) unsgined int (C) double word = 3 bit, longint C CD-audio 6 bit, 44. kbpsch74 DVD-audio, Hi-Res audio 4 bit, 9 kbps4.7gb Facebook Byte/ 8 kb Instagram Byte/ 3 MB iphone 7s (5.5 inch) Byte/ 6 MB ipad Pro 9.7 inch Byte/ 9 MB /
2 dpi= mm 0.0 mm bit/l7mm 89mm 5 MB Byte/ 5 fps 0 Mbps HDTV fps.5 Gbps 4K fps 6 Gbps IEEE bit = 4 byte 4 byte 3 bit s e e e 3... e 7 e 8 f f 3 f 4... f 3 f (7) 54 = ± f f 3 4! f 4 e 7 e 6!e /
3 e e!e 8 = ( ) = 0 = ± f f 3 4! f 4 6 ( e e!e 8 ) = ( ) = 55 3 s = 0, f f 3! f 4 s =, f f 3! f 4 = ( 00!0) = = ( 00!0) = ( f f 3! f 4 ) 00!0 = NAN (not a number = ! 7 = bit = 8 byte s e e... e 0 e f f 3... f 5 f e e!e = ( ) ( e e!e ) ( 0) =06 3 /
4 = ( ) s f f 3 4! f 53 e 0 e 9!e 03 ( e e!e ) = ( ) = 0 5 s = 0, f f 3! f 53 s =, f f 3! f 53 5 = ± f f 3 4! f ( e e!e ) = ( ) = 047 = ( 00!0) = = ( 00!0) = ( f f 3! f 53 ) 00!0 = NAN (not a number = ! 03 = π= /
5 elementary functions eponential function : logarithmic function : ln log log e trigonometric functions ep( ) = e sine function : sin cosine function : tangent function : cos tan cosecant function : secant function : cotangent function : inverse trigonometric functions sec = cos arcsine function : arcsin sin arccosine function : arccos cos arctangent function : arctan tan csc arccosecant function : arccosec cosec arcsecant function : arcsec sec arccotangent function : arccot cot hyperbolic functions cosec = sin cot = tan hyperbolic sine function : hyperbolic cosine function : hyperbolic tangent function : hyperbolic secant function : sinh = e e cosh = e e tanh = e e e e hyperbolic cosecant function : cosech = e e sech = e e 5 /
6 hyperbolic cotangent function : inverse hyperbolic functions coth = e e e e inverse hyperbolic sine function : arcsinh = sinh = ln ± e y e y = 0 e y = ± inverse hyperbolic cosine function : arccosh = cosh = ln( ± ) e y e y = 0 e y = ± inverse hyperbolic tangent function : arctanh = tanh = ln ( e y ) = e y e y = inverse hyperbolic cosecant function : arccosech = cosech = ln ± inverse hyperbolic secant function : arcsech = sech = ln ± inverse hyperbolic cotangent function : arccoth = coth = ln y = a y = ep ln a 6 /
7 ep ep( ) =! 3 3! 4 4!! N N! ep =! =.5 = !! 3! =.666!! 3! 4! = !! 3! 4! 5! =.76666!!! 3!!! = ! f ( ) = f ( 0) f ' 0! f '' 0 3! f ''' 0 4! f (4) 0 N! f (N ) ( 0) = a j j 3 a j = f ( j ) 0 j! 4! N N j = 0 tan tan = 3 5 7! 7 /
8 tan = ! 3 = =.555! 3 =.55737! 5 7 y = a 0 a a! y = a 0 a ( a a ) ( a 3 a )! = a 0 = a 0 = a 0 a = a 0 ( a a ) ( a a a a 3 ) ( a 4 a a 3 a )! ( a 3 a ) ( a 4 a )! = a 0 a ( a a ) a 3 a a = a 0 ( a a ) ( a 3 a )!! ( a a ) ( a 3 a )! a ( a a ) ( a 3 a ) ( a 4 a )! ( a a ) ( a 3 a )! [ ] a ( a a ) ( a a ) ( a 3 a )! ( a 3 a ) ( a 4 a )! a = a 0 ( a a ) ( a a a a 3 ) [( a 4 a a 3 a ) ( a 3 a a a )]! ( a 3 a ) ( a 4 a )! { } a ( a a ) ( a 3 a a a ) ( a 3 a ) ( a 4 a )! [( a 4 a a 3 a ) ( a 3 a a a )]! 8 /
9 a = a 0 ( a a ) ( a 3 a a a ) [( a a a a 4 3 ) ( a 3 a a a ) a 3 a ]! [( a 4 a a 3 a ) ( a 3 a a a )]! f f 3 f ' ( ) = lim f f ( ) f h h 0 h ( ) = d ep ln d = = ln h = ep ln f ( 3) = 3 ln = ! f ( 3) f = ln = = ! numerical differential 9 /
10 S = b a f d numerical integral quadrature w f a b a S b a ( ) w f a ( b a)! w N f ( a ( b a) N ) mid-point method S = b a N f a 0.5( b a) N ( b a) f a.5 b a N! f a N 0.5 N ep ln t = u = t t v = u u y = v u f ( ) = a 0 a a a 3 3 a /
11 0 f ( ) = a 0 a a ( a 3 a 4 ) f ( ) = a 0 a a a 3 3 a 4 4 3! 4! = a 0 a a 3 a 3 a 4 f Horner 4 b c = 0 = b ± b c b > 0 c > 0 c b b c b = c = =, b b c = b b c c = b b c Mathematica /
12 /
0104.pages
0 5 9 07 0 bit 8, 6, 3 bit byte = 8 bit, char (C )BYTEFORTRAN) 055, -87 word = 6 bit int (C) INTEGER (FORTRAN) -3,7683,767 unsgined int (C) 065,535 double word = 3 bit, longint (C )-,47,483,648,47,483,647
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