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Extends the concepts of Calculus I and II that deal with functions of a single variable to multi-variable functions, vector-valued functions and vector fields. Vectors and vector-valued functions, the dot and cross products, curves in space and the calculus of vector-valued functions. Multi-variable functions, limits, continuity, and differentiation. Partial derivatives, directional derivatives, the gradient, Lagrange multipliers and optimization. Double and triple integrals in Cartesian, polar and spherical coordinates. Vector fields and the fundamental theorems of vector calculus developed, line and surface integrals, Green's theorem, Stokes's theorem, and the divergence theorem.
MATH.1320 Calculus II, or MATH.2250 Calculus C.