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 16 Operators for wave motions

16.1 The mathematical operator

We are used to the concept of a mathematical function: a procedure that, when applied to a given number (known as its argument), generates another number as its result. We routinely use the sine and cosine functions, the logarithm and exponent, factorial, powers, roots and so on; they are so fundamental to the language of mathematics that we rarely give them a second thought.

The argument here refers to the variable upon which a function depends. The same term is also used specifically to describe the phase of a complex number. For the function f (φ) ≡ exp(), the variable φ will be the argument in both senses.

Many of the functions with which we are already familiar map a single ...

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