Timings and Venue:
- Timing: Tuesday, Thursday and Friday, 11:00 a.m. to 12:00 noon
- Venue: Room G2, Old Physics building.
Instructor
Instructor: Siddhartha Gadgil
e-mail: siddhartha DOT gadgil At gmail DOT com
Assignments:
An assignment will be posted every Friday morning, and will be due on the next Friday.
Syllabus:
Basic notions from set theory, countable and uncountable sets. Metric spaces: definition and examples, basic topological notions. The topology of R^n: topology induced by norms, the Heine-Borel theorem, connected sets. Sequences and series: essential definitions, absolute versus conditional convergence of series, some tests of convergence of series. Continuous functions: properties, the sequential and the open-set characterizations of continuity, uniform continuity. Differentiation in one variable. The Riemann integral: formal definitions and properties, continuous functions and integration, the Fundamental Theorem of Calculus. Uniform convergence: definition, motivations and examples, uniform convergence and integration, the Weierstrass Approximation Theorem.
References:
- Terence Tao, Analysis I, 3rd Edition, Texts and Readings in Mathematics, vol. 37, Hindustan Book Agency, 2014
- Terence Tao: Analysis II, 3rd Edition, Texts and Readings in Mathematics, vol. 38, Hindustan Book Agency, 2014.
- T.M. Apostol: Mathematical Analysis, 2nd edition, Narosa.