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Details of MA2101 (Autumn 2020)

Level: 2 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA2101 Analysis I Soumya Bhattacharya

Syllabus
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 \mathbbR: Open and closed sets; interior, boundary and closure of a set; Bolzano-Weierstrass theorem; sequential definition of compactness and the Heine-Borel theorem.

Limit of a Function: Limit of a function, elementary properties of limits.

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

References


  1. Al-Gwaiz, M.A. and Elsanousi, S.A., Elements of Real Analysis, CRC Press.

  2. Apostol, T.M., Mathematical Analysis, Narosa Publishers.

  3. Bartle, R.G. and Sherbert, D.R., Introduction to Real Analysis, Wiley.

  4. Berberian, S.K., A First Course in Real Analysis, Springer.

  5. Denlinger, C.G., Elements of Real Analysis, Jones and Bartlett Publishers.

  6. Goldberg, R.R., Methods of Real Analysis, Oxford \& IBH Publishing.

  7. Howie, J.M., Real Analysis, Springer-Verlag.

  8. Kumar, A. and Kumaresan, S., A Basic Course in Real Analysis, CRC Press.

  9. Morrey, C.B. and Protter, M.H., A First Course in Real Analysis, Springer-Verlag.

  10. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill.


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

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