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EVALUATION OF LINE INTEGRALS
Contours with Singularities on the Path
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analytic solution application approximation associated assumed asymptotic base vectors becomes boundary conditions branch called cartesian characteristic circle coefficients complex components computed consider consistent constant continuous contour convergent coordinate system covariant curve defined definition depends derivative determine difference differential equation domain equal error evaluate Example exists expansion expression Figure Find finite difference finite element formula function given gives grid independent indicates integral interval introduce involving known leading limit linear matrix method node Note numerical obtain operator original parameter partial positive presented problem procedure referred region relation requires residue respect Riemann integral satisfy second order shown singular solution solved space step Substitution Table Taylor tensor term Theorem tion transformation unknowns value problem variable vectors written yields zero