Introduction to Numerical Methods: Errors and their computation: Round off error, Truncation error, Absolute error, Relative error and Percentage error. Solution of algebraic and transcendental equations: Bisection, Regula-Falsi, Secant and Newton-Raphson methods.

Numerical solutions for system of linear equations: Norms: Vector norms and Matrix norms-L1, L2 and L∞, Ill conditioned linear system, condition number. Solution of system of linear equations: Gauss Seidel method and LUdecomposition method. Eigenvalues and Eigen vectors: Rayleigh power method, Jacobi’s method.

Interpolation: Finite differences, interpolation using Newton Gregary forward and Newton Gregary backward difference formulae, Newton’s divided difference. Lagrange interpolation formulae, piecewise interpolation-linear and quadratic.

Differential Equations of First and Higher Order: Linear and Bernoulli`s differential equations. Exact and reducible to exact differential equations with integrating factors on 1/N (∂M/∂y − ∂N/∂x) and −1/M (∂M/∂y − ∂N/∂x). Homogeneous and non-homogeneous Differential equations of higher order with constant coefficients. Inverse differential operators – e^ax, sin(ax+b), cos(ax+b) and xⁿ.

Numerical Integration and Numerical Solution of Differential Equations: Numerical integration: Trapezoidal, Simpson’s 1/3rd, Simpson’s 3/8th rule and Weddle’s rule. Numerical solution of ordinary differential equations of first order and first degree – Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order and Milne’s predictor-corrector method.