Details of MA2101 (Autumn 2017)
Level: 2 | Type: Theory | Credits: 3.0 |
Course Code | Course Name | Instructor(s) |
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MA2101 | Analysis I | Shirshendu Chowdhury |
Syllabus |
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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. |
References |
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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. | Programme | Semester No | Course Choice |
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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 |