Differential Calculus: Functions of several variables, Open sets, Limits and continuity, Derivatives of a scalar field with respect to a vector, Directional derivatives, Partial derivatives, Total derivative, Gradient of a scalar field, Level sets and Tangent planes, Derivatives of vector fields, Chain rules for derivatives, Mean value theorem, Derivatives of functions defined implicitly. Applications of Differential Calculus: Maxima, Minima, Saddle points, Stationary points, Lagrange's mult