 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2005/4/i/solution

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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