Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doubt about linear functions

  1. Jan 4, 2012 #1
    Re: The difference between linear and non linear differential equation

    Hello,

    I was going through the same problem. From what I can see on the net, one of the relations a linear function has to express is:

    f(u + v) = f(u) + f(v)

    Now if f(x) = ax + b is linear then

    f(u + v) = a(u+v) + 2b

    So f(u + v) is not equal to f(u ) + f(v).

    So why is f(x) = ax + b linear as it fails this criteria?

    Sorry for this stupid question......

    Thanks,
    Luc
     
  2. jcsd
  3. Jan 4, 2012 #2
    Re: The difference between linear and non linear differential equation

    It is not a stupid question. The definition above is exactly the definition of a linear function, i.e. a function f that satisfies f( cx + y ) = c f ( x ) + f ( y ) ( note that you can pull the scalar out, so that functions of the form cx are linear )
    the map f ( x ) = ax + b is taught to us in grade school as a linear function on the basis that it draws a line. Actually though, it is called an "affine function" ( it acts essentially like a linear map though, the map will satisfy all the properties if you simply translate everything by b ).
    In the context of differential equations, both cases are known as "linear equations"
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Doubt about linear functions
  1. Linear Functions (Replies: 2)

  2. Linear Functionals (Replies: 13)

  3. Linear Functions (Replies: 3)

Loading...