Good Morning Students! Myself Dr. Gajendra Purohit Today we are going to discuss Numerical Analysis There two important topics in it One is Numerical Differentiation & another is Numerical integration Before that, there are some basic topics The most important topic in numerical analysis is Interpolation With this comes the concepts of Integration and its formulas we will discuss all this Today we will start Interpolation My other videos you can see by clicking on the i-tab in which I have uploaded videos on mathematics and higher mathematics like Complex, Fourier matrices, Partial differential equation, partial differentiation Gama, beta functions There is a complete playlist of videos I think my videos are helping you in exams my objective is mainly on concepts and how to solve questions students who are preparing for competitive exams I will make separate videos on those topics Let's see what is Interpolation the population given Now if its asked like this when values of an interval are asked when we will take out its values, there are various formulas In interpolation, there are two types of concepts So students in Equal interval if asked to take out the population in 1973 you will check the trend of population that how it is increased the formula used here is Newton Forward because we are looking at the forward trend and finding the value if asked to take out the population of 2008 we will see the backward trend here we are looking at the backward trend the formula used here is Newton Backward to take out the centre value the formula used here is for central difference for that, there are 3 formulas we will study newton forward and newton backward my next video will be on central difference Now let's talk about unequal interval I will make a separate video on it if this difference is not equal in this type of questions first, you have to see, whether the interval is equal or unequal So these formulas will not be used here Formulas used here will be One more formula used here is Newton Divided Difference we can use that also my next video will be on this topic All these concepts of interpolation can be asked for derivatives also if its asked you have to take out derivative Then we will talk about how ordinary differential equation is solved with numerical analysis so we will discuss all these topics you can click on i-tab for the videos