Interpretation of The Contour Integral
The contour integral can be interpreted in two ways:
- as the total change in the argument of f(z) as z travels around C, explaining the name of the theorem; this follows from
and the relation between arguments and logarithms.
- as 2πi times the winding number of the path foC around the origin, using the substitution w = f(z):
Read more about this topic: Argument Principle
Famous quotes containing the words interpretation of, contour and/or integral:
“Philosophers have actually devoted themselves, in the main, neither to perceiving the world, nor to spinning webs of conceptual theory, but to interpreting the meaning of the civilizations which they have represented, and to attempting the interpretation of whatever minds in the universe, human or divine, they believed to be real.”
—Josiah Royce (1855–1916)
“The living language is like a cowpath: it is the creation of the cows themselves, who, having created it, follow it or depart from it according to their whims or their needs. From daily use, the path undergoes change. A cow is under no obligation to stay in the narrow path she helped make, following the contour of the land, but she often profits by staying with it and she would be handicapped if she didn’t know where it was or where it led to.”
—E.B. (Elwyn Brooks)
“An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
—Henry David Thoreau (1817–1862)