Real number: infimum and supremum, completeness principle, rational number system. Archimedes principle, extended real number system (introduction only), Schwartz and Minkowski inequalities (in Rn).



Set and functions (review), countability.



Sequences and subsequences: Cauchy sequence, complete metrics space.



Metrics topology in R and Rn - limit point, interior points, open set and closed set, compact set, Bolzano-Weierstrass and Heine Borel theorems, connected set.



Continuous functions: continuity in a compact domain, continuity in a connected domain; uniform continuity, functions sequence and functions series, point by point convergence and uniformity, Weierstrass-M test; Weierstrass approximation theorem.



General metrics space (definition and examples).



References:

1. Wade, W.R. (2004). An Introduction to Analysis (3rd Edition). Pearson Prentice Hall.

2. Bartle, R.G., & Sherbert, D.R. (2000). Introduction to Real Analysis (3rd Edition). Wiley & Sons.

3. Mattuck, A.P. (1998). Introduction to Analysis. Prentice Hall.