Details of MA2101 (Autumn 2016)

Level: 2 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA2101 Analysis I Satyaki Mazumder

Real Numbers: Introduction to the real number field, supremum, infimum, completeness axiom; basic properties of real numbers, decimal expansion; construction of real numbers.

Sequences and Series: Convergence of a sequence, Cauchy sequences and subsequences; absolute and conditional convergence of an infinite series, Riemanns theorem, various tests of convergence.

Point-set Topology of R: Open sets, closed sets; interior, boundary and closure of a set; the Bolzano-Weierstrass theorem; compactness and the Heine-Borel theorem.

Limit of a function: Limit of a function, elementary properties of limit.

Continuity: Continuous functions, elementary properties of continuous functions, intermediate value theorem, uniform continuity, properties of continuous functions defined on compact sets.

1. Apostol, T. M., Mathematical Analysis (2nd Edition), Narosa Publishers, 1996.

2. Howie, J. M., Real Analysis, Springer Undergraduate Mathematics Series, Springer-Verlag, 2008.

3. Morrey, C. B. and Protter, M. H., A First Course in Real Analysis (2nd Edition), Undergraduate Texts in Mathematics, Springer-Verlag, 2004.

4. Rudin, W., Principles of Mathematical Analysis (3rd Edition), International Series in Pure and Applied Mathematics, McGraw-Hill, 1976.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 3 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed