## Details of MA2201 (Spring 2020)

Level: 2 |
Type: Theory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
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MA2201 |
Analysis II |
Sushil Gorai |

Syllabus |
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Differentiation: Definition and basic properties, higher order derivatives, Leibnitzs theorem on
successive differentiation. Mean Value Theorems: Rolles theorem, Lagranges and Cauchys mean value theorems, Taylors theorem, computation of Taylors series, LHopitals rule Maxima and Minima: Maxima and minima of a function of one variable, saddle points, applications. Integration: Riemann integral viewed as an area, partitions, upper and lower integrals, Riemann integrability of a function, basic properties of Riemann integrals, mean value theorems for Riemann integrals, fundamental theorem of integral calculus, change of variable formula and integration by parts, improper Riemann integral, beta and gamma functions. Sequence of functions: Uniform convergence, convergence and continuity, Weierstrass approximation theorem. |

References |
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Suggested Texts:
1. Al-Gwaiz, M.A. and Elsanousi, S.A., Elements of Real Analysis, CRC Press. 2. Apostol, T.M., Calculus I (2nd edition), Narosa Publishers. 3. Howie, J.M., Real Analysis, Springer-Verlag. 4. Morrey, C.B. and Protter, M.H., A First Course in Real Analysis, Springer-Verlag 5. Rudin, W., Principles of Mathematical Analysis (3rd Edition), McGraw-Hill. |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 2 | Not Allowed |

2 | IP | 4 | Not Allowed |

3 | IP | 6 | Not Allowed |

4 | MR | 2 | Not Allowed |

5 | MR | 4 | Not Allowed |

6 | MS | 4 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |