1. SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
Conditions for convergence of an iterative method, rate of convergence of an iterative method, comparison of
False Position, Newton-Raphson and Secant methods, conversion of a divergent functional iteration scheme
into a convergent one.
Newton-Raphson method for solution of nonlinear system of equations.
2. NUMERICAL METHODS IN LINEAR ALGEBRA
Computation of determinant, pivot, partial and complete pivoting technique, triangularization algorithm,
triangular decomposition of a matrix, properties of triangular matrices,
Least squares curve fittings,
Solution of homogeneous linear equations.
3. NUMERICAL DIFFERENTIATION AND INTEGRATION
Numerical differentiation using finite differences, numerical integration, Newton-Cote’s formula, trapezoidal
rule for integration, Simpson's 1/3 rule, Simpson's 3/8 rule.
4. NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS
Numerical solution of first order ordinary differential equation using Taylor's series, Picard's, Euler's,
Modified Euler's method, Runge -Kutta method of fourth order.