method for finding numerical roots of equations. You start with an estimate
of the root, you then replace the function by its tangent (a linear
approximation) find the zero of the equation of the tangent, to give a
new approximation to the root. Repeat this process as often as needed.
Because the computation with a linear approximation to a function is2.why would you use the linear approximation of a function than the actual function
usually simpler than with the function itself. Or to use known results from
a linear theory to give an approximate result in a non-linear case.
A nice example which is probably beyond your current experience is the
Kalman filter, which is an optimal estimator for certain types of linear
systems. With mildly non-linear systems one linearises about an appropriate
estimate, and then uses the KF equations to give a sub-optimal but good
estimator for the non-linear case (known as the Extended Kalman Filter (EKF)).