Course: MAT 212 2.0 Real Analysis I (Compulsory)
Course content: Review of the real number system, boundedness, supremum and infimum of a set, completeness axiom, concept of area under a curve, partitions of closed intervals, upper and lower Riemann sums and related results, upper and lower Riemann integrals and related results, Riemann Integrability and the Riemann integral, examples for non-integrable functions, Riemann’s criterion for integrability, Integrability theorems (Integrability of continuous functions, piecewise continuous functions and functions with finitely many discontinuities), Anti derivatives, Fundamental theorem of Calculus and its applications, Improper integrals, Riemann-Stieltjes integral.
Recommended Readings: Elementary Classical Analysis – Jerrold E. Marsden, Principles of Mathematical Analysis – Walter Rudin, Calculus: Early Transcendentals – James Stewart, Introduction to Real Analysis- Donald R. Sherbert and Robert G. Bartle