ABSTRACT
Parameters can be represented as lumped parameters, meaning that spatial variations are ignored (as in homogeneous systems), whereas distributed parameters are valid for variation in behavior from point to point throughout the system. Steady-state models describe the situation where the accumulation term (the time derivative) is zero. For steady-state models with lumped parameters, algebraic equations are used. For steady state as well as nonsteady-state models with distributed parameters, partial differential equations (PDEs) are needed. For steady-state models with one distributed parameter and for nonsteadystate models with lumped parameters ordinary differential equations (ODEs) are needed. We are often interested in the variation of a quantity y (e.g., concentration) as a function of the
variation of another quantity x (e.g., time). Suppose we have a function y¼ f (x) and we want to know how y varies when x is varied. This is conveniently expressed in a differential equation:
y0 ¼ dy dx
¼ lim|{z} Dx!0
