Syllabus
Differential calculus of several variables: the metric space En, vector-valued function of several variables, limits and continuity, partial derivatives and differentials, chain rules, the gradient, directional derivatives, Taylor´s theorem, extreme values, differentiation of implicit functions.
Multiple integral: double and triple integrals, evaluation - iterated integrals, integration in polar, cylindrical and spherical coordinates, applications.
Calculus of vector fields: vector fields, basic curves and surfaces in the space, conservative vector fields and potencial functions, applications of line integrals.
Sequences and serier: convergence properties of sequences, infinit series of constants, nonnegative series - the integral, the comparison and the ratio tests, alternating series and absolute convergence, power series, Taylor series.
Annotation
Is a continuation of the course MatC, the main focus will be improper integral, series and the calculus of functions of several variables.