... Differential equations are equations that involve derivatives of unknown functions f~=sinh-I(.!!.)=ln(U+~) a a .Ja2 +u2 +a ±E lnlu+.Ju2 +a W.f.Ju ±a2 du= !! Ju 2 ­ DIFFERENTIAL EQUATIONS B.Volumes ... or r = 2csin8 if a = O B Roses I Polar equations r = ccosn8 or r = csinn8 n determines the number of petals on the rose C Cardioids & Limacons I Polar equations r = a ± bcos8 or r = a ± bsin8 ... have the same derivative Jf(x~ = F(x) + C IF and onlv IF, r(x) C =f(x) IV Fundamental Theorem of Calculus A If f(x) is an integrable continuous function on the interval [a, b], and if F(x) is a...
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... for 2-d z polar coordinates r ϕ E Use of Calculus in Physics Methods from calculus are used in y physics definitions, and the derivations of equations and laws θ Physical meanings of calculus expressions: ... capacitors; determine voltage and current properties Key Equations and Concepts: CREDITS Author: Mark Jackson, PhD Chemical Physics M.A Physics, Harvard University BEHAVIOR OF LIGHT f f I Spherical ... direction b Scalar: Magnitude only, no direction Number and unit a Physical data, constants and equations have numerical values and units b A correct answer must include the correct numerical...
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