### MATH 5205. Advanced Calculus II

Course Code MATE 5205 Advanced Calculus II 3 3 per week MATE 5201, MATE 4031 (recommended) Series of real and complex numbers. Sequences and series of functions, uniform convergence, power series. The Euclidean space: elementary topology of $R^n$$R^n$. Notions on metric spaces. Functions of several variables: continuity and differentiation. Contraction mapping theorem. The implicit function theorem. Integration on $R^n$$R^n$. Fundamental theorems of vector calculus