Numerical Methods In Civil Engineering

COURSE OBJECTIVES

The aim of the course is to develop a sound understanding of the various numerical techniques, principles and their application to Civil engineering problems.

Fundamental principles and basics of numerical methods will be covered.
Some of the important numerical techniques and its applications will be discussed in details.

LEARNING OUTCOMES

• 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.