A-Level Maths: F6-01 [Reduction to Linear Form: The Basic Idea]

in this video I want to give a basic idea introduction to reduction in linear form so let's say you've collected some data okay you've collected some data and you've made a graph of this data okay so let's say graph looks something like this for example okay some points might be little bit over the place but you get the idea right okay so then you might go right well there seems to be having collected this data some kind of relationship the fact that as one's increasing the others increasing both it's curved it's not a straight line okay and you might think well I could fit a curve to this perhaps okay and if I know that I've got a curve I might then be able to predict to extrapolate to beyond that date or think of interpolating some data items in between okay so be able to figure those out so you might think right well this looks like there's a curve okay some curve that the data is attached to and you might think well let's say it looks like some kind of polynomial for example so we're gonna say that it's something like perhaps fitting a function of y equals a X to the n okay so hey just multiplying okay allowing that stretch and you've got this X to the N okay so because you don't know what that power is necessarily going to be and so you think right okay well if that's the case and now what I want to do is not to check whether it's the case because at the moment that's all I'm in good thinking that it's going to be off that form but we don't know what a is and we don't know what n is so what we're going to do is we are going to use a linearization of this so we go through a process of taking logarithms of both sides the we're gonna take logarithms is because of that power okay makes it easier for a cell so I'm gonna go through this process in the coming videos of how we get from that and we go through this process of reducing to linear form okay so what you're gonna get is something that might look like this okay some kind of y equals MX plus C a straight line equation that's what we would be hoping okay if you can get from that to that not saying that every equation that you start with every curve you can get to y equals MX plus C there are some that do and this is one of those cases okay so you get to a straight line equation now the reason why we might want a straight line equation is because it's much easier then to get the gradient and y-intercept of a straight line so what we then do is be part on new coordinates x and y and it gives us a straight line equation from which we can find C from which we can work out the gradient M okay and then if we could write a in terms of M all the rather M in terms of a and C in terms of N or whatever okay then we can work backwards to figure out what a and n are and that will then tell me the equation of this curve so this is the concept of reducing to linear form it's because we've got this data we think this curve will attach to it but the curving question has unknowns and we need to figure those out easiest way to do that is to reduce it to this linear form estimate the value of C and M based on the data that I have and then I can work backwards to get a and n and then solve the quiet problem and from that because I've now got an equation I can then say like what would the value of y be when X is this say I'd be able to find that point or that point or that point on the curve again I could use it for predictions if I needed to so that's like the basic idea of the process and in these videos we're going to go through the mechanics of how we actually do it

Channel: TLMaths

Views: 10,045

Keywords: A-Level Maths, Reduction to Linear Form

Id: 6QI6QcearEw

Length: 4min 52sec (292 seconds)

Published: Fri Sep 08 2017