Syllabus
1. Improper integrals.
2. 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.
3. 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.
4. Multiple integral: double and triple integrals, evaluation - iterated integrals, integration in polar, cylindrical and spherical coordinates, applications.
5. Calculus of vector fields: vector fields, basic curves and surfaces in the space, line integrals, line integrals of vector fields, the fundamental theorem of line integrals, conservative vector fields and potencial functions, applications of line integrals.
Annotation
As a continuation of the course from the previous term S710P04A the main focus will be improper integral, series and the calculus of functions of several variables.