Excerpt from Applied Calculus: Principles and Applications, Essentials for Students and Engineers
If a choice must be made between the ability to solve equations (including integration processes) and the far more rare ability to set up equations to represent established facts... and laws, there can be little question as to which type of ability should be cultivated. The latter is of higher order and is likely to include the former. Engineers, physicists, inventors and men of science generally find it difficult to translate their observations into language which the pure mathematician can understand. In fact, such translation usually involves the writing of the equation: an undertaking beyond the capacity equally of the non-mathematical scientist and the pure mathematician. Integration of the equation, once set up, the mathematician will undertake; conceiv ably, so might a machine. Fruitful deductions and rules of practice result. The difficulty of realizing these results arises not from difficulties in moving about the symbols, but from inability on the part of nearly all persons to state facts in terms of symbols. It is as if no harmonist knew a melody and no melodist knew a note. This book aims to keep fact and symbol in close association, so that the student will never use the latter without being conscious of the former. It may then be expected that he will ultimately be able to visualize the symbolic expression when the fact is known.
Apart from the references in the text and in footnotes, acknowledgment is here made of the clarifying and logical ideas embodied in the books on the Calculus by Gibson, by Taylor, and by Townsend and Goodenough; also in H edrick's paper on the Calculus without Symbols.
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