Real Analysis–II (MTH 453) offered in the second semester of the M.Sc. Mathematics programme at Mangalore University (February 18 to June 20, 2026) develops advanced foundations of analysis beyond basic integration and limits. The course begins with the Riemann–Stieltjes integral, its properties, and applications to vector-valued functions and rectifiable curves. It then explores sequences and series of functions, emphasizing uniform convergence and its impact on continuity, integration, and differentiation. Students study function spaces, equicontinuity, and the Weierstrass approximation theorem alongside classical special functions. The course concludes with functions of several variables, covering partial and directional derivatives, and major results including the Contraction Principle, Inverse Function Theorem, and Implicit Function Theorem.
- Teacher: Sri. Bhargava K.