Numerical Methods In Civil Engineering

By Prof.Y.M.Desai & Prof.T.I.Eldo | Indian Institute of Technology Bombay

Learners enrolled: 1544

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

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	16 weeks
Category :	Annual Refresher Programme in Teaching (ARPIT)
Credit Points :	6
Level :	Postgraduate
Start Date :	03 Sep 2019
End Date :	31 Dec 2019
Exam Date :

Page Visits

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.

Books and references

Chapra, S. C. and Canale, R. P.: Numerical Methods for Engineers, McGraw Hill, 2014
Jain, M.K., Iyengar, S.R.K. and Jain, R. K., Numerical Methods for Scientific and Engineering Computation, Wiley Easter Ltd., New Delhi, 1995.
Desai, Y. M., Eldho, T. I. and Shah, A. H.: Finite Element Method with Applications in Engineering, Pearson, 2013.
Reddy, J.N., Finite Element Method, McGraw-Hill Inc, New York, 1993.
Brebbia, C.A., Telles, J.C.F. and Wrobel, L.C., Boundary Element Techniques- Theory and Applications in Engineering, Springer-Verlag, Berlin , 1984.

Instructor bio

Prof.Y.M.Desai & Prof.T.I.Eldo

Indian Institute of Technology Bombay

Dr Yogesh Desai is JK & MJ Mehta Chair Professor of Structural Engineering, Department of Civil Engineering, IIT Bombay. He has over 35 years of teaching and research experience in the areas of Structural Engineering and Computational Mechanics. He has published over 200 research papers in reputed journals and conferences. He has co-authored three popular books and is recipient of several awards for excellence in teaching and academics.

Dr Eldho is an Institute Chair Professor & Head of Department of Civil Engineering, IIT Bombay. He has 29 years of experience in the area of water resources and environmental engineering as Scientist, Professor and Consultant. He works in the areas of Fluid Mechanics, Coastal Hydrodynamics and Climate Change Impact on Water Resources, CFD, Groundwater Flow and Contaminant transport. He has guided 27 Ph.Ds, 4 Postdoctoral Fellows and 54 Masters theses and presently guiding 14 more Ph.D students in various areas. He has published more than 450 research papers in various International Journals and Conferences. He has developed and offered 25 courses and number of short term courses for college teachers and working professionals. He has also developed two popular video courses on “Fluid Mechanics” and “Watershed Management”. Prof. Eldho serves as an Editor/ Associate Editor and Editorial Board Member of a number of Indian and International Journals and has worked as a reviewer for more than 50 national and international Journals in the recent past. He is also a research proposal reviewer for many research organizations and delivered several invited/ keynote lectures at various national and international organizations and conferences. Dr. Eldho has co-authored two popular text books and contributed 12 book chapters in various edited books. He is recipient of many prestigious awards including Eminent Water Resources Scientist, constituted by Indian Water Resources Society in 2018.

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