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...Lecture notes for math multivariable calculus j dimock dept of mathematics sunyatbualo bualo ny december contents vectors functions several variables limits partial derivatives the chain rule implicit function theorem i ii inverse maxima and minima dierentiation under integral sign leibniz variations vector valued other coordinate systems line integrals double triple parametrized surfaces surface area change in r gradient divergence applications more stoke s still general complex numbers denitions properties polar form special cauchy riemann equations analyticity formula higher inequalities real fourier laplace transforms we start with some a number x is positive zero or negative rational irrational denote set all label points on once pick an origin unit length are also called scalars next dene pairs elements plane pair orthogonal axes dimensional can be represented by arrows from to point triples space three especially one might em phasize that writing it bold face arrow but refrain d...