Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2005 / 4 / i

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- Solution i

Solution

For a smooth curve

γ : [a, b] \to C

and continuous

f

on its image, the contour integral is defined by

\int_{γ} f (z) d z = \int_{a}^{b} f (γ (t)) γ^{'} (t) d t .

The derivative carries the direction and speed of traversal; the complex-valued real-parameter integral is defined by integrating its real and imaginary parts.

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