Study of the conceptual underpinnings of multivariable differential and integral calculus.  Topics of study include three-dimensional analytic geometry and vectors, quadratic surfaces, arc length and curvature, limits and continuity, partial derivatives and their applications, tangent planes, optimization problems and Lagrange multipliers, multiple integrals, vector fields, line and surface integrals, Green’s theorem, Stokes’ theorem, the divergence theorem. Particular attention is paid to visualization and geometry.  Formal proofs of important theorems are discussed with special emphasis on how to adapt the material to the intended audience.

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