11. The Gauss Bonnet integrand is the Euler class. 12. It is most efficient when the peaks of the integrand are well-localized. 13. In the limit, the integrand becomes a constant, so that integration is trivial 14. By the fundamental lemma of the calculus of variations, the integrand must vanish identically: 15. Manipulating this will give you the integrand . 16. To simplify the calculations, one first takes the variation of the square of the integrand . 17. The integral in this solution simplifies considerably when certain special cases of the integrand are considered. 18. Shouldn't the " c " from the integrand return in the result? 19. In Clenshaw Curtis quadrature, the integrand is approximated by expanding it in terms of Chebyshev polynomials. 20. This connection can be seen by Wick rotating the integrand in the exponential of the path integral.
