Many important and significant problems in engineering, the physical
sciences, and the social sciences, when formulated in mathematical
terms, require the determination of a function satisfying an equation
containing one or more derivatives of the unknown function. Such
equations are called differential equations. The most
familiar example is Newton's law 
. If 
is the
position at time 
of a particle of mass 
acted on by a
force 
, then we obtain
where the force 
may be a function of t,u, and the
velocity 
. To determine the motion of a particle subject to a
given force F it is necessary to find a function u satisfying the
differential equation (1).
The main purpose of this course is to discuss numerical approaches to solve these differential equations. In many real-world cases, the differential equations do not have a closed form solution. We start with a review of some of the terminology.
