MATH201 Lecture : ch6-p1.pdf
16 Apr 2014
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Some physical phenomena can adequately be described by means of ordinary di erential equations (abbre- viated odes). For example, motion of a mass on a spring is governed by newton"s law of force: f = ma in which f = kx is the force of the spring and a = d2x/dt2 is the acceleration. That is which is an ode for the position x of the mass at time t. m d2x dt2 = kx, While some physical phenomena are adequately modelled by odes, most physical phenomena require a more sophisticated mathematical model. Examples of physical phenomena for which odes provide inadequate models include: the spread of pollutants in the environment, the ow of air over an aircraft, the structure of the hydrogen atom, the cooking of a turkey. For these, and in fact most physical phenomena, a more appropriate model is furnished by a collection of partial di erential equations (abbreviated pdes) together with initial and/or boundary conditions.
