MAT 212 2.0 Real Analysis I – Department of Mathematics

Course: MAT 212 2.0 Real Analysis I (Compulsory)

Course Content:

Real functions, Boundedness, limits and continuity, Riemann integrability and the Riemann integral (Darboux approach), Non integrable functions, Properties of the Riemann integral, Anti derivatives, Fundamental theorem of calculus and it’s applications, Improper integrals, Test for convergence of improper integrals, Riemann’s approach to integration, Equivalence of Riemann and Darboux approaches, Numerical methods of integration, Arc length formula.

Recommend Readings:

1. Ross, K. A., Elementary Analysis: The Theory of Calculus 2^nd ed. Springer (Undergraduate Texts in Mathematics), 2013
2. Abbott S., Understanding Analysis 2^nd ed. Corr. 2nd printing, Springer (Undergraduate Texts in Mathematics), 2016
3. Shahriari,S., Approximately Calculus, American Mathematical Society, 2006
4. Rudin, W., The Principles of Mathematical Analysis, 3^rd ed. International Series in Pure & Applied Mathematics, 2006
5. Bartle, R. G., & Sherbert, D. R., Introduction to Real Analysis, 4^th ed. Wiley 2011
6. Hammack, R., BOOK OF PROOF, 3^rd ed. Richard Hammack, 2018 (https://www.people.vcu.edu/~rhammack/BookOfProof/)