Direct Methods
Direct methods involve the calculation of the integral by means of methods similar to those in calculating line integrals in several-variable calculus. This means that we use the following method:
- parametrizing the contour
- The contour is parametrized by a differentiable complex-valued function of real variables, or the contour is broken up into pieces and parametrized separately
- substitution of the parametrization into the integrand
- Substituting the parametrization into the integrand transforms the integral into an integral of one real variable.
- direct evaluation
- The integral is evaluated in a method akin to a real-variable integral.
Read more about this topic: Methods Of Contour Integration
Famous quotes containing the words direct and/or methods:
“Computer mediation seems to bathe action in a more conditional light: perhaps it happened; perhaps it didn’t. Without the layered richness of direct sensory engagement, the symbolic medium seems thin, flat, and fragile.”
—Shoshana Zuboff (b. 1951)
“Cold and hunger seem more friendly to my nature than those methods which men have adopted and advise to ward them off.”
—Henry David Thoreau (1817–1862)