- A lumped system is one in which the dependent variables of
interest are a function of time alone. In general, this will mean
solving a set of ordinary differential equations (ODEs)
- A
*distributed*system is one in which all dependent variables are functions of time*and*one or more spatial variables. In this case, we will be solving partial differential equations (PDEs)

For example, consider the following two systems:

- The first system is a
*distributed*system, consisting of an infinitely thin string, supported at both ends; the dependent variable, the vertical position of the string is indexed continuously in both space and time. - The second system, a series of ``beads'' connected by massless
string segments, constrained to move vertically, can be thought of as
a
*lumped*system, perhaps an approximation to the continuous string. - For electrical systems, consider the difference between a lumped RLC network and a transmission line

- The importance of
*lumped approximations*to distributed systems will become obvious later, especially for waveguide-based physical modeling, because it enables one to cut computational costs by solving ODEs at a few points, rather than a full PDE (generally much more costly)

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