Multivariable Calculus 7.5 credits

The course presents the basics of the Calculus in several variables. The course focuses on the following topics: - Curves and surfaces in implicit form and parameter form (in particular the quadrics) - Basic set-theoretical concepts. Polar, cylindrical and spherical coordinates - Functions of several variables, level curves and surfaces - Limits and continuity, partial derivatives - Gradient, differentiability, directional derivatives and linerization - The chain rule, change of variables, the nabla differential operator, curl and divergence. Higher order partial derivatives, the Laplace and wave PDEs - Second-order Taylor polynomial, classification of critical points and identification of local extremes - Optimization on compact domains, optimization subject to constraints, Lagrange multipliers - Double and triple integrals, Fubini evaluation, change of variables - Basic calculus of vector-valued functions, line and surface integrals, conservative fields, potentials - The Green's, Gauss' divergence and Stokes formulas.