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, Gauss-Elimination, LU Decomposition and Gauss-Seidel, Conjugate gradient method. 

 Eigenvalues and Eigenvectors: Jacobi Method for symmetric matrices, Power method for arbitrary matrices. 

 Interpolation and Approximation: Lagrange, Newton’s Divided Difference, Newton’s Forward and Backward interpolations and cubic splines,

 Differentiation and Integration: Numerical differentiation, Maxima and Minima, Numerical integration, Newton-Cotes formulas, Romberg integration, Gaussian integration,

 Solutions of Ordinary Differential Equations: Initial Value problems, Euler methods, Modified Euler method and Fourth order Runge-Kutta method. Boundary value problems using Forward Difference operators.

 Solutions of Partial Differential equations: Elliptic, Parabolic and Hyperbolic equations implicit and explicit methods. 

Text Books

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

Reference books

• R.L. Burden, J. D. Faires, Numerical Analysis, Richard Stratton, 2011, 9th edition.
• 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.
• S. S. Sastry, Introductory methods of Numerical Analysis, 2012, PHI Publishers, 5th edition,