Contents
Introductions to Matrices. Brief introduction of matrices. Symmetric and matrices. Introduction to elementary row operations. Echelon and reduced echelon forms. The rank of a matrix. The inverse of a matrix using elementary row operations.
System of Linear Equations. System of non-homogeneous and homogeneous linear equations. Gaussian elimination method, Gauss Jordan method. Consistence criterion for the solution of a homogeneous and non-homogeneous system of linear equations. Application of systems of linear equations.
Error Analysis: Introduction, floating points, errors, types of errors.
Solution of Non-Linear Equations: Bisection method, Regula-Falsi method, Newton-Raphson method, fixed-point iterative method.
Solution of Linear Algebraic Equations: Iterative methods: Jaccobi’s method, Guass-Seidal method.
Eigen Values and Eigen Vectors: Power method.
Interpolation and Extrapolation: Differences: Forward, backward, central, operators, and their relations. Newton’s forward interpolation formula. Newton’s backward interpolation formula, Newton’s divided difference formula, Lagrange’s interpolation formula.
Numerical Differentiation: Newton’s forward and backward differentiation formulae.
Numerical Quadrature: Trapezoidal rule, Simpson’s one-third rule, Simpson’s three-eighth rule. Numerical Solution of Ordinary Differential Equations: Taylor series method, Euler’s and its modified methods, Runge-Kutta methods