Numerical Methods In Civil Engineering

• Better understanding of various methods
• Exposure to various numerical methods for performing tasks, such as interpolation, differentiation, integration, solution of linear and nonlinear equations, solution of differential and integral equations
• Ability to apply numerical methods to obtain approximate solutions to mathematical problems.
• Ability to analyze and evaluate accuracy of various numerical methods and their applicability
• Exposure to established and advanced numerical methods like Finite Element Method, Meshfree Methods and Boundary Element Methods
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COURSE LAYOUT

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.