The modern approach to the study of the phenomena of the physical world, essentially the methods of Galileo, Newton, Leibniz, and their successors, relies heavily upon the use of mathematics as the language of science. The description of physical processes in this language leads to a number of functional equations, of which the most familiar are ordinary differential equations.

For the reading and effective utilization of a significant quantity of the material in this book, we require only a modicum of mathematical training; say that acquired in a good course in advanced calculus: Naturally, the more mathematical training the reader has, the easier will be his fask and the more he will absorb. A rudimentary knowledge of the uses of the computer will also be useful. Above all, we require a certain amount of intellectual maturity - whatever this indefinable quality is - but no more than what we know to be possessed by those currently engaged in the application of mathematical techniques to biology, economics, engineering, physics, and so on. Our aim is to reduce the painful and time-consuming task of obtaining the numerical solution of large classes of functional equations that occur repeatedly in the description of scientific problems to a routine chore, a chore which can be delegated to assistants. In some fortunate cases, our methods can be carried out with the aid of a slide rule or a desk computer. In other cases, we may require the numerical integration of a system of ordinary differential equations or of a system of linear algebraic equations. This is the maximum of computational sophistication that we require.
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