Course

Unit 1

Roots of Transcendental and Polynomial Equations: Incremental Search Method, Method of Bisection, Methods Based on Linear Interpolation, Newton-Raphson Method, Systems of nonlinear Equations

Unit 2

Interpolation: Lagrange, Newtons Divided Difference, Newtons Forward and Backward interpolations and cubic splines. Differentiation and Integration: Numerical differentiation, Maxima and Minima, Numerical integration, Newton-Cotes formulas, Romberg integration, Gaussian integration,

Unit 3

Solution of System of Linear Algebraic Equations, Gauss-Elimination, LU Decomposition, Iterative methods: Pivoting, Gauss-Seidel.Eigenvalues and Eigenvectors: Jacobi Method for symmetric matrices, Power method and Inverse Power Methods for arbitrary matrices.

Unit 4

Solutions of Ordinary Differential Equations: Initial Value problems, Euler methods, Modified Euler method and Fourth order Runge-Kutta method. Finite difference methods. Boundary value problems using Forward Difference operators. First order PDE, Solutions of Partial Differential equations: Elliptic, Parabolic equations.

Text Books / References

Text Books:

1. Numerical Methods in Engineering with Python, Jaan Kiusalaas, Cambridge University Press, 2010.
2. K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical methods for scientific and Engineering computation, New Age International Publishers, 2007, 5th edition.

Reference Books:

1. L. Burden, J. D. Faires, Numerical Analysis, Richard Stratton, 2011, 9th edition.
2. D. Conte and Carl de Boor, ‘Elementary Numerical Analysis; An Algorithmic Approach’. International series in Pune and Applied Mathematics, McGraw Hill Book Co., 1980.
3. S. Sastry, Introductory methods of Numerical Analysis, 2012, PHI Publishers, 5th edition,

This course introduces several techniques of numerical methods, algorithms for finding roots of equations or system of equations, Interpolation, Numerical differentiation, Numerical Integration, decomposing matrices, solving differential equations numerically.

Course Outcomes: After successful completion of the course, students will be able to

• CO1 : Find roots of transcendental and nonlinear equations.
• CO2 : Interpolate the given data; compute numerical derivatives and numerical integrations.
• CO3 : Perform matrix related methods in solving linear equations and finding eigenvalues.
• CO4 : Apply single step, multistep and finite difference methods to solve ODE and PDE.

CO-PO Mapping:

Evaluation Pattern