Multivariable calculus. Continuity at a point. Continuity in a domain. Partial and directional derivatives. Total differential. Differentiable functions, Jacobian matrix. Composite functions. Homogeneous functions. Higher order partial derivatives. Schwarz theorem. Implicit function theorem.  Inverse function theorem. Change of variables, Jacobian. Mean value theorem, Taylor theorem, local extrema. Conditional extrema and Lagrange multipliers. Vector valued functions, continuity and differentiation. Scalar and vector fields. Differential operators, grad, div, curl in several coordinate systems.

In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences.