## Details of ID4104 (Autumn 2018)

Level: 4 |
Type: Laboratory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
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ID4104 |
Numerical Analysis Laboratory |
Koel Das |

Syllabus |
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Numerical Analysis
Solution of Non-linear Equations: Bisection method, fixed point iteration method, Newton-Raphson, secant, regula-falsi methods. Solution of Systems of Linear Equations: Gauss elimination method, Thomas algorithm, Gauss-Jacobi and Gauss-Seidel methods. Solution of Systems of Non- linear equations: Fixed-point method and Newtons method. Least Square Method: Fitting of linear, exponential, polynomial curves, fitting of curves which are not linear in constants (either directly or after re parametrization). Interpolation: Newtons forward, backward and divided difference formulae, Lagranges method, Gauss, Stirling and Bessels formulae, Spline interpolation. Numerical Differentiation: Formulae based on Newtons forward, backward, divided difference, and Lagranges formulas. Numerical Integration: Trapezoidal rule, Simpsons 1/3rd and 3/8th rules, Weddles rule; quadrature formulas based on Stirlings and Bessels interpolation formulas. Solution of Differential Equations: Taylors series method, Picards method and Runge-Kutta methods (1st, 2nd and 4th orders) for solving ODEs, Picards method and Runge-Kutta method (4th order) for solving system of ODEs; Predictor-Corrector method due to Milne and Adams-Bashforth-Moulton, finite difference method and shooting method for solving BVPs; solution of parabolic, elliptic and hyperbolic PDEs. Eigenvalues and Eigenvectors: Power method, Jacobis method, Givens method, Householders method. |

References |
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Suggested Texts/Reference Books:
1. Atkinson, K., Elementary Numerical Analysis (3rd Edition), Wiley, 2006. 2. Conte, S. D. and De Boor, C., Elementary Numerical Analysis : An algorithmic Approach, Tata McGraw- Hill, 2005. 3. Froberg, C. E., Introduction to Numerical Analysis, Addison-Wesley, 1965. 4. Scarborough, J. B., Numerical Mathematical Analysis (6th Edition), Johns Hopkins University Press, 1966. |

#### Course Credit Options

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

1 | IP | 1 | Elective |

2 | IP | 3 | Not Allowed |

3 | IP | 5 | Not Allowed |

4 | MR | 1 | Not Allowed |

5 | MR | 3 | Not Allowed |

6 | MS | 7 | Elective |

7 | RS | 1 | Elective |

8 | RS | 2 | Not Allowed |