1. In the former, we specify both the function and the normal derivative. 2. "' Continuity of normal derivatives of double layer potentials . "' 3. Taking the boundary values of both sides and their normal derivative yields 2 equations. 4. It is often easier to work in differential form and then convert back to normal derivatives. 5. Since the mean of the normal derivative of a harmonic function over a circle is zero. 6. The value of the normal derivative at a boundary point can be computed from inside or outside ?. 7. For partial differential equations, Cauchy boundary conditions specify both the function and the normal derivative on the boundary. 8. On the tubular neighbourhood of " ?, the "' normal derivative "'is defined by 9. On the other hand, on each boundary curve the contribution is the integral of the normal derivative along the boundary. 10. The tangential derivatives on the outer curves are nowhere vanishing by the Cauchy-Riemann equations, since the normal derivatives are nowhere vanishing.