공학수학 원서 pdf

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공학수학10판 원서

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  Systems of Units. Some Important Conversion Factors The most important systems of units are shown in the table below. The mks system is also known asthe  International System of Units (abbreviated SI  ), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used. System of unitsLengthMassTimeForcecgs systemcentimeter (cm)gram (g)second (s)dynemks systemmeter (m)kilogram (kg)second (s)newton (nt)Engineering systemfoot (ft)slugsecond (s)pound (lb) 1 inch (in.)  2.540000 cm1 foot (ft)  12 in.  30.480000 cm1 yard (yd)  3 ft  91.440000 cm1 statute mile (mi)  5280 ft  1.609344 km1 nautical mile  6080 ft  1.853184 km1 acre  4840 yd 2  4046.8564 m 2 1 mi 2  640 acres  2.5899881 km 2 1 fluid ounce  1/128 U.S. gallon  231/128 in. 3  29.573730 cm 3 1 U.S. gallon  4 quarts (liq)  8 pints (liq)  128 fl oz  3785.4118 cm 3 1 British Imperial and Canadian gallon  1.200949 U.S. gallons  4546.087 cm 3 1 slug  14.59390 kg1 pound (lb)  4.448444 nt1 newton (nt)  10 5 dynes1 British thermal unit (Btu)  1054.35 joules1 joule  10 7 ergs1 calorie (cal)  4.1840 joules1 kilowatt-hour (kWh)  3414.4 Btu  3.6  • 10 6  joules1 horsepower (hp)  2542.48 Btu/h  178.298 cal/sec  0.74570 kW1 kilowatt (kW)  1000 watts  3414.43 Btu/h  238.662 cal/s°F  °C  • 1.8  321°  60   3600   0.017453293 radian For further details see, for example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics. 9th ed., Hoboken,N. J: Wiley, 2011. See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical andElectronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at www.ieee.org.  Integration  u v  dx   u v    u  v  dx (by parts)   x  n dx    c ( n  1)   dx   ln    x    c  e ax dx    e ax  c  sin  x dx   cos  x   c  cos  x dx   sin  x   c  tan  x dx   ln   cos  x    c  cot  x dx   ln   sin  x    c  sec  x dx   ln   sec  x   tan  x    c  csc  x dx   ln   csc  x   cot  x    c    arctan   c    arcsin   c    arcsinh   c    arccosh   c  sin 2  x dx   1 _ 2  x   1 _ 4 sin2  x   c  cos 2  x dx   1 _ 2  x   1 _ 4 sin2  x   c  tan 2  x dx   tan  x    x   c  cot 2  x dx   cot  x    x   c  ln  x dx    x  ln  x    x   c  e ax sin  bx dx   ( a sin  bx   b cos  bx  )  c  e ax cos  bx dx   ( a cos  bx   b sin  bx  )  ce ax a 2  b 2 e ax a 2  b 2  x   adx      x  2         a    2    x   adx      x  2         a    2    x   adx     a   2         x     2    x   a 1  adx    x  2  a 2 1 a 1  x  x  n  1 n  1 Differentiation ( cu )   cu  ( c constant)( u  v )   u   v  ( u v )   u  v  u v  ( )    • (Chain rule)(  x  n )   nx  n  1 ( e x )   e x ( e ax )   ae ax ( a x )   a x ln  a (sin  x  )   cos  x  (cos  x  )   sin  x  (tan  x  )   sec 2  x  (cot  x  )   csc 2  x  (sinh  x  )   cosh  x  (cosh  x  )   sinh  x  (ln  x  )   (log a  x  )   (arcsin  x  )   (arccos  x  )   (arctan  x  )   (arccot  x  )   1  1   x  2 1  1   x  2 1    1        x     2   1    1        x     2   log a  e   x  1   x dy  dx du  dydu  dx u  v  u v   v 2 u  v
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