One can ensure proper discontinuity in the first derivative by integrating the defining differential equation (i.e., Eq. *) from x = s − − ε ε to x = s + ε ε and taking the limit as ε ε goes to zero. Note that we only integrate the second derivative as the remaining term will be continuous by construction. c 3 ⋅ ⋅ ( − − k sin ⁡ ⁡ k s ) − − c 2 ⋅ ⋅ ( k cos ⁡ ⁡ k s ) = 1