The main purpose for this course is to introduce the following concepts: 1 Functions of several variables, their limits, continuity and partial differentiation. 2 Double integral, double integral in polar coordinates and application 3 Triple integral, triple integral in cylindrical and spherical coordinates and their applications 4 Sequences, their limits. Series, geometrical series, convergence tests for positive term series, alternating series and absolute and conditional convergence of series. . 5 Power series, power series representation of functions 6 McLaurin and Taylor series.
Cartesian, cylindrical and spherical coordinate systems. Functions of two and three variables, limits and continuity, partial derivatives, the chain rule, extrema of functions of two variables, Lagrange multipliers. Double integrals, moments and center of mass, double integrals in polar coordinates, triple integrals, application of triple integrals, triple integrals in cylindrical and spherical coordinates, surface area. Sequences, infinite series, convergence tests, representation of functions by power series, Taylor and Maclaurin series, the binomial series.
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