Mathematical Analysis (Advanced Calculus and Theory of Real Variables I)


           This course is the last of the series of courses in calculus. It serves in general to review and extend fundamental concepts already presented in elementary calculus. It gives a systematic, modern approach to differential and integral calculus of functions and transformations in several variables. It covers R as a complete ordered field, point set topology, limits and continuity, the derivatives, multivariable differential calculus, implicit functions and extrema problems, convergence of sequences and series of real numbers, sequences and series of functions, uniform convergence, power series, functions of bounded variation and rectifiable curves, Riemann-Stieltjes integrals; interchanging of limit operations, multiple integration, improper integrals and transformations.