MATH-275 Final: MATH 275 Boise State Final formulas

• School: Boise State University
• Department: Mathematics
• Course: MATH-275
• Professor: All

Document Summary

Polar coordinates: x = r cos( ) y = r sin( ) r2 = x2 + y2 da = rdrd . Cylindrical coordinates: x = r cos( ) y = r sin( ) z = z r2 = x2 + y2 dv = rdrd dz. Spherical coordinates: x = sin( ) cos( ) y = sin( ) sin( ) z = cos( ) r = sin( ) 2 = x2 + y2 + z2 dv = 2 sin( )d d d . Vector fields: f (x, y, z) = p (x, y, z) i + q(x, y, z) j + r(x, y, z) k. Divergence: div( f ) = f = p. Curl: curl( f ) = f = (cid:16) r. Ftcvf: f (q) f (p ) = zc. F d s = zzzb curl( f ) d s div( f )dv. Curves: r (t) = x(t) i + y(t) j + z(t) k.