| Course Name | Numerical Methods |
| Course Code | 25MAT312 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 6 |
| Credits | 3 |
| Campus | Mysuru |
Roots of Transcendental and Polynomial Equations: Bisection method, Iteration methods based on first degree equation, Rate of convergence, system of nonlinear equations.
Solution of System of Linear Algebraic Equations: Iteration methods
Eigenvalues and Eigenvectors: Jacobi Method for symmetric matrices, Power method for arbitrary matrices.
(Sections : 2.2, 2.3, 2.5, 2.7, 3.4, 3.5, 3.6)
Interpolation and Approximation: Lagrange and Newton interpolation for unequal intervals, Finite difference operators, Interpolating polynomials using finite differences.
(Sections: 4.2, 4.3,4.4)
Differentiation and Integration: Numerical differentiation, Methods based on interpolation, Numerical integration, Methods based on undetermined coefficients.
Sections: (5.2, 5.6, 5.7, 5.8)
Solutions of Ordinary Differential Equations: Initial Value problems, single step methods, Taylor series method, Second, Third and Fourth order Runge-Kutta methods.
(Sections: 6.1,6.3, 6.4)
Solutions of Partial Differential equations: Elliptic partial Differential equations, Parabolic partial differential equations, Hyperbolic partial differential equations.
(Sections: 12.1, 12.2, 12.3)
Course Objectives:
Course Outcomes
| COs | Description |
| CO1 | Apply appropriate numerical methods to solve the problem with most accuracy |
| CO2 | Demostrate solving interpolation with equal interval problems by various numerical methods. Estimate the missing terms through interpolation methods. |
| CO3 | Explain the derivation of Trapozoidal rule, Simpson’s 1/3 – rule, Simpson’s 3/8 – rule, and Weddle’s rules from General Quadrature formula |
| CO4 | Apply Euler, Taylor and Runge-Kutta methods to find the solution of ordinary differential equation. |
| CO5 | Analyse the accuracy and efficiency of solution for different methods in numerical analysis with |
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO2 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO3 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO4 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO5 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
TEXT BOOKS:
1 M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical methods for scientific and Engineering computation, New Age International Publishers, 2007, 5th edition.
2 R.L. Burden, J. D. Faires, Numerical Analysis, Richard Stratton, 2011, 9th edition.
REFERENCES:
1 S.D. Conte and Carl de Boor, ‘Elementary Numerical Analysis; An Algorithmic Approach’. International series in Pune and Applied Mathematics, McGraw Hill Book Co., 1980.
2 Kandasamy P, Thilagavathi.K and Gunavathi. K. ‘Numerical Methods’- S. Chand and Company Ltd., New Delhi- Revised Edition 2007.
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