MTH640 Real Analyses
Lead Faculty: Dr. Igor Ya Subbotin
Course Description
Topics include real and complex number systems, elements of point-set topology of Euclidean space, numerical sequences and series, continuity and differentiability for functions of one and several variables. The Riemann-Stieltjes integral as a generalization of the Riemann integral, sequences and series of functions, and Fourier series will be studied as well.
Learning Outcomes
- Evaluate ordered sets, real and complex fields
- Apply main concepts of metric spaces and their topology to concrete problems
- Interpret the connectedness, compactness and Weierstrass theorem
- Evaluate the Cauchy sequences, completeness of real numbers, convergence and absolute convergence of series
- Interpret concepts of limits, continuity of functions in metric spaces, and their properties, differentiation and integration
- Interpret uniform convergence of functions and Stone-Weierstrass theorem
- Evaluate the use of special functions
- Elaborate the Contraction Mapping Theorem, The Inverse Function and the Implicit Function Theorems.
