Historical development of Numerical techniques, role in investigations, research and design in the field of civil engineering development of algorithm/ flow charts for following methods for the solution of linear simultaneous equation- Gaussian elimination method, Gauss-Jordan matrix inversion method, Gauss-Siedel method and Factorization method.

Development of algorithm for Bisection method. Newton-Raphson method and its applications for solution of nonlinear algebraic and transcendental equations from problems in hydraulics, irrigation engineering, structural engineering and environmental engineering.

Numerical differentiation and integration Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson’s 1/3 rule Romberg’s Method Two-point and three-point Gaussian quadrature formulae Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules. Trapezoidal rule, Simpson’s one-third and their application for computation of area of BMD drawn for statically determinate beams.

New Marks method for computation of slopes and deflections in statically determinate beams. Development of algorithm and application of solution of ordinary differential equation to civil engineering problems by Euler’s method, Runge Kutta 4th order method

Introduction, expression of derivatives by finite difference: backward differences, forward differences, and central differences. Application of finite difference method for analysis of statically determinate beams, statically indeterminate beams, Buckling of columns, Beams on elastic foundation.