 Hi, welcome to this NPTEL course on Numerical Analysis. I am Bhaskar from the Department of Mathematics IIT Bombay. This is a 12 week long course consisting of around 30 to 36 hours of video lectures including some tutorial sessions. Each week we will have 5 to 6 each of around half an hour of duration. We will also have some live sessions to help you out with solving problems. There will be weekly assignments and one exam at the end of the course. The course suits mathematical sciences and engineering students from advanced undergraduate to beginning graduate level. This course is also accessible to anybody with good calculus knowledge and an elementary knowledge of linear algebra. Also some experience in writing simple computer course will make the learning process more enjoyable. Well coming to the subject Numerical Analysis is a branch of mathematics with mainly two components with equal emphasis. One is to develop numerical methods for a given mathematical problem to obtain approximate solutions. Note that a numerical method is a mathematical method written in the form of an algorithm that can be implemented as computer code to generate numerical solutions. Once we see that a numerical method will provide us with approximate solution to our problem, the next task of the subject is to analyze and handle the error involved in the numerical solution compared to the exact solution of the problem. To summarize numerical analysis is a mathematical subject that deals with developing numerical methods for various mathematical problems and their error analysis. Hence a numerical analyst should be good at developing and analyzing numerical methods for various mathematical problems. This course aims to make a starting point to train ourselves as numerical analysts. So, we will learn the subject by developing numerical methods for some simple mathematical problems like finding the solution of a non-singular linear system, computing eigenvalues and eigenvectors of an invertible matrix, finding a simple solution to a non-linear equation, approximating a continuous function by polynomials and piecewise polynomials, integration and differentiation of some class of functions and solving some differential equations. We will also learn some mathematical tools to do error analysis. It is also desirable to have exposure to computer programming. So, we will also learn to code some numerical methods using Python language. I am sure you will enjoy learning the subject with us. I hope to see you on our course. Thank you.