Analytic Functions of Several Variables
One can define analytic functions in several variables by means of power series in those variables (see power series). Analytic functions of several variables have some of the same properties as analytic functions of one variable. However, especially for complex analytic functions, new and interesting phenomena show up when working in 2 or more dimensions. For instance, zero sets of complex analytic functions in more than one variable are never discrete.
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Famous quotes containing the words analytic, functions and/or variables:
““You, that have not lived in thought but deed,
Can have the purity of a natural force,
But I, whose virtues are the definitions
Of the analytic mind, can neither close
The eye of the mind nor keep my tongue from speech.””
—William Butler Yeats (1865–1939)
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)