Numerical Methods In Civil Engineering

Module 1: Mathematical Modeling:

(02 Lectures)Introduction, Mathematical tools and techniques, Advanced modeling applications

Module 2: Numerical Approximation and Solution of Equations: (10 Lectures)

 Numerical approximation, Error analysis, Curve fitting, Interpolation and Extrapolation, Numerical differentiation and integration, Solution of linear and nonlinear equations.

Module 3: Numerical Solution of Ordinary and Partial Differential Equations: (10 Lectures) 

Classification of differential equations, Analytical solution of differential equations, Numerical Solution of differential equations: Time-marching schemes: Single step method, multi-step method; Runge - Kutta methods.

Module 4: Approximate Methods: Finite Difference and Finite Element Methods: (10 Lectures)

Various finite difference schemes, implicit and explicit methods, method of weighted residuals, Collocation methods, Method of Least squares, Method of Galerkin, Raleigh-Ritz methods, Applications to engineering problems.

Module 5: Advanced Numerical Methods: (12 Lectures)
Introduction to Finite element method, Introduction to Boundary Element Method, Introduction to Meshfree Methods; Applications to engineering problems.