tailieunhanh - Ebook Advanced engineering mathematics (10th edition): Part 1

(BQ) Part 1 book "Advanced engineering mathematics" has contents: First-Order ODEs, second-Order linear ODEs; higher order linear ODEs; systems of ODEs, phase plane, qualitative methods; laplace transforms; vector differential calculus - Grad, Div, Curl; partial differential equations (PDEs), fourier series, integrals, and transforms,.and other contents. | 11/4/10 12:05 PM Page 2 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 as the 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 units Length Mass Time Force cgs system centimeter (cm) gram (g) second (s) dyne mks system meter (m) kilogram (kg) second (s) newton (nt) Engineering system foot (ft) slug second (s) pound (lb) 1 inch (in.) ϭ cm 1 foot (ft) ϭ 12 in. ϭ cm 1 yard (yd) ϭ 3 ft ϭ cm 1 statute mile (mi) ϭ 5280 ft ϭ km 1 nautical mile ϭ 6080 ft ϭ km 1 acre ϭ 4840 yd2 ϭ m2 1 mi2 ϭ 640 acres ϭ km2 1 fluid ounce ϭ 1/128 . gallon ϭ 231/128 ϭ cm3 1 . gallon ϭ 4 quarts (liq) ϭ 8 pints (liq) ϭ 128 fl oz ϭ cm3 1 British Imperial and Canadian gallon ϭ . gallons ϭ cm3 1 slug ϭ kg 1 pound (lb) ϭ nt 1 newton (nt) ϭ 105 dynes 1 British thermal unit (Btu) ϭ joules 1 joule ϭ 107 ergs 1 calorie (cal) ϭ joules 1 kilowatt-hour (kWh) ϭ Btu ϭ • 106 joules 1 horsepower (hp) ϭ Btu/h ϭ cal/sec ϭ kW 1 kilowatt (kW) ϭ 1000 watts ϭ Btu/h ϭ cal/s °F ϭ °C • ϩ 32 1° ϭ 60Ј ϭ 3600Љ ϭ 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 and Electronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at . 11/4/10 12:05 PM Page 3 Differentiation (cu)Ј ϭ cuЈ (c constant) Integration ͵ uvЈ dx ϭ uv Ϫ ͵ uЈv dx (by parts) ͵ x dx ϭ nx ϩ 1 ϩ c (n Ϫ1) nϩ1 (u ϩ v)Ј ϭ uЈ ϩ vЈ (uv)Ј ϭ uЈv