## Details of MA2101 (Autumn 2016)

Level: 2 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

MA2101 |
Analysis I |
Satyaki Mazumder |

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 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 |
---|

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 |
---|---|---|---|

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 |