ANALYSIS I

Review of Real and Complex numbers systems, Topology of R, Continuity and differentiability, Mean value theorem, Intermediate value theorem. The Riemann-Stieltjes integral. Introduction to functions of several variables, differentiablility, directional and total derivatives. Sequences and series   of  functions, uniform convergence, the Weierstrass approximation theorem.

Books

• Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, 1986.
• Royden,  H. L.,  Real  Analysis,  Macmillan, 1988.