Advanced Calculus I

Course content

Topology of R, R2 and R 3 . Functions of several variables; limits and continuity. Partial derivatives, directional derivatives, gradients. Differentials and the tangent plane: the Fundamental Lemma, approximations. The Mean Value, implicit and Inverse function theorems. Extreme values. Introduction to vector differential calculus: the gradient, divergence and curl. Curvilinear coordinates.