Analytical Methods - A Civil Engineering Course under the National Programme on Technology Enhanced Learning

This Civil Engineering Course under the National Programme on Technology Enhanced Learning (NPTEL) on the broad subject of Analytical Methods in Civil Engineering is being carried out by Indian Institute of Technology’s and the Indian Institute of Science, Bangalore as a collaborative project supported by the Ministry of Human Resource Development (Government of India) to enhance the quality of engineering education in the country, by developing curriculum based video and web courses. In these web based lectures, the authors have developed the subject in detail and in stages in a student-friendly manner. The broad group of Analytical Methods in Civil Engineering is structured into modules on the following topics:

Numerical Methods in Civil Engineering

This course by IIT Kharagpur provides a broad background to numerical methods common to various branches of civil engineering. It starts with the core concepts of error estimate and accuracy of numerical solutions and thereafter deals with methods of solution of linear and non-linear equations. Both direct and iterative solution methods are discussed.

The numerical solution of partial differential equations is introduced after a brief review of canonical partial differential equations and well known analytical techniques for their solution, stressing when and why numerical solutions are necessary. Finite difference operators are introduced and used to solve typical initial and boundary value problems. The finite element method is introduced as a generic method for the numerical solution of partial differential equations. The course syllabus can be viewed at the NPTEL website here

Probability Methods in Civil Engineering

This course by IIT Guwahati deals with the probabilistic elements that are to be dealt with as part of civil engineering curriculum. In the initial few lectures, basic concepts on probability and random variables are covered in detail.

Various discrete and continuous probability distributions that are commonly used in the fields of Structural Engineering, Environmental Engineering, Geotechnical Engineering, Water Resource Engineering, and Transportation Engineering are presented in detail. Topics such as statistics and their distributions are also covered with relevant examples. The course also covers hypothesis testing which is equally important when some conclusions are to be drawn from the experimental/field data. The course syllabus can be viewed at the NPTEL website here

This course as offered by IIT Kharagpur deals with the concept of probability and different probabilistic models. Concept and definition of random variables and different functions of random variables are covered in the initial part of the course. Both univariate and multivariate functions are discussed. Concept of joint, marginal and conditional probability distributions, moments, expectations, correlation are discussed. 

Both discrete (binomial distribution, poisson’s distribution) and continuous distribution functions (normal, lognormal, exponential distribution, gamma distribution) are discussed. Concept of central limit theorem is introduced. The course ends with the discussion of statistics and sampling. The course syllabus can be viewed at the NPTEL website here

Finite Element Analysis

This course by IIT Kharagpur apprises the students about the basics of the Finite Element Technique, a numerical tool for the solution of different classes of problems. Different application areas are dealt with after introducing the basic aspects of the method. However, major emphasis is on the solution of problems related to Civil Engineering. It is intended to cover the analysis methodologies for 1-D, 2-D and 3-D problems with the advantages and disadvantages clearly spelt out. The aim is also to enable the students to be in a position to develop computer codes for any physical problem using Finite Element Technique. The course syllabus can be viewed at the NPTEL website here

This course by IIT Madras on finite element analysis covers fundamental concepts and presents it as a tool to find approximate solution of differential equations and thus can be used by students from a variety of disciplines. Applications include analysis of structural frameworks, stress analysis, heat flow and fluid flow. The course syllabus can be viewed at the NPTEL website here