Calculus of several variables
This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.
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Differentiation of Vectors
Functions of Several Variables
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3-space assume boundary centered chain rule Chapter circle of radius column vector component constant continuous function cos(xy cos2 counterclockwise critical point definition denote differentiable function differential operator disc of radius distance divergence theorem dot product dx dy dy dx equal equation Example Exercise exists expression Figure Find the integral finite number function defined function f(x,y geometric given grad f(P gradient graph Green's theorem Hence inequalities integral of F interpretation interval inverse mapping Jacobian matrix Let F Let f(x Let f(x,y Let g level curves line segment linear map located vector maximum multiplied normal vector notation obtain open set origin parallelogram parametrization partial derivatives perpendicular polar coordinates potential function Proof prove quadratic form rectangle respect satisfy set of points Show shown on Fig sin(xy spanned sphere of radius square Suppose surface tangent plane unit vector vector field write