## Details of MA1202 (Spring 2019)

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

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

MA1202 |
Mathematical Methods I |
Ananda Dasgupta, Ratikanta Behera |

Syllabus |
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Part I: Matrix Theory
1.Linear System: System of linear equations and its solvability, Gauss elimination and Gauss-Jordan elimination methods. 2.Matrices & Determinants: Rank and inverse 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. Part II: Ordinary Differential Equations 1.First Order Equations: Linear equations, integrating factor, Bernoullis Equation. Clairauts Equation. 2.Second Order Equations: Linear equations with constant coefficients, general solutions, non-homogenous equations, c omplementary function and particular integral. Linear equations with variable coefficients -Power series solutions. Part III: Calculus II 1.Calculus with complex numbers. Differentiability -Cauchy Riemann conditions. Analytic functions. Singularities. Cauchy's theorem. Residue theorem. Applications to the calculation of sums and integrals. |

References |
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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 | 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 | 2 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |