Analyis for functions of one real variable; linear geometry; linear algebra.
Norms, distances, equivalent norms and equivalent distances.
Limits and continuity of functions of several real variables.
Regular curves, simple curves, equivalences among curves, paths, unit tangent vector to regular paths, curve lenghts, integrals of continuous functions along paths; work of a field along a path..
Differential calculus for functions of several real variables: directional derivatives and their geometric meaning, partial derivatives, gradients, differentiation rules, tangent hyperplanes and their geometric meanings, Schwarz Theorem, Taylor formula, quadratic forms, local maxima and minima.
Implicit Function Theorem, Inverse Function Theorem, smooth surfaces, Lagrange Theorem. Elementary notions about multiple integrals: definitions, reduction theorem, changes of variables.