## Details of MA1101 (Autumn 2016)

Level: 1 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
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MA1101 |
Mathematics I |
Narayan Banerjee |

Syllabus |
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Part I: Calculus I
1. Curves & Surfaces: Curve tracing, tangent & normal to a curve. Surfaces, parametric representations, normal. 2. Functions of Several Variables: Partial derivatives, commutativity of mixed partial derivatives, total differential, applications to approximating functions. Exact and closed differential, gradient, curl and divergence. 3. Multiple Integrals: Double and triple integrals, iterated integrals. Change of variable formula, curvilinear co-ordinate systems; polar, spherical, cylindrical coordinates. 4. Vector Analysis: Line integral and surface integral. Greens Theorem, Stokes Theorem and Divergence theorem. Part II: Matrix Theory 1. Linear System: System of linear equations and its solvability, Gauss elimination and Gauss-Jordan elimination methods. 2. Matrices & Determinants: Rank, inverse and transpose of a matrix. Some important classes of matrices: Symmetric, anti-symmetric, orthogonal, Hermitian and unitary matrices. Determinant of a matrix. Similarity transformation. 3. Eigenvalues: Eigenvalues and eigenvectors. Calculation of eigenvalues, Cayley-Hamilton theorem. Diagonalizability of matrices. Part III: Calculus II 1. Sequence & Series: Notion of convergence, geometric and zeta series, tests of convergence. 2. Taylors Series: Taylors expansion of a function, calculation of power series. |

References |
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Suggested Texts / Reference Books:
1. Apostol, T. M., Calculus I (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2011. 2. Apostol, T. M., Calculus II (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2007. 3. Arfken, G. B., Weber, H. & Harris, F., Essential Mathematical Methods for Physicists and Engineers, Academic Press, 2003. 4. Boas, M. L., Mathematical Methods In The Physical Sciences (3rd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2006. 5. Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010. |

#### 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 | 1 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |