Approximations and round off errors:
Significant figures, accuracy and precision, error definitions, round off errors and truncation errors. Mathematical modeling and engineering problem solving: Simple mathematical model, Conservation laws of engineering. Roots of polynomial-polynomials in engineering and science, Muller’s method, Bairstow’s Method Graeffe’s root squaring method.
Roots of Equations:
False position method, Newton- Raphson method. Multiple roots by Newton-Raphson method. Simple fixed point iteration method- Acceleration of convergence- ∆2 - Aitken’s method. Numerical Differentiation and Numerical Integration: Newton –Cotes and Guassian Quadrature Integration formulae, Integration of Equations, Romberg integration, Numerical Differentiation Applied to Engineering problems, High Accuracy differentiation formulae.
Numerical Solution for Partial Differential Equations:
Classification of second order partial differential equations. Solution of one dimensional heat equation by explicit method and Crank-Nicolson method. Solution one dimensional wave equation and two-dimensional Laplace equation by explicit method.
System of linear algebraic equations and eigen value problems:
Introduction, Direct methods, Gauss elimination method, triangularization method, Cholesky method, Partition method, Error analysis for direct methods. Eigen values and eigen vectors: bounds on eigen values, Jacobi method for symmetric matrices, Givens and Householder’s method for symmetric matrices. Power method and Inverse power method.
Linear Transformation:
Introduction to linear transformation. The matrix of linear transformation, linear models in science and engineering. Orthogonality and least squares: inner product, length and orthogonality, orthogonal sets, orthogonal projections. Gram-Schmidt process, least-square problems, inner product spaces.