  We develop techniques, based on differential geometry, to compute holomorphic
Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds
defined as complete intersections in projective spaces. It is shown explicitly
how these techniques relate to algebraic methods for computing holomorphic
Yukawa couplings. We apply our methods to various examples and evaluate the
holomorphic Yukawa couplings explicitly as functions of the complex structure
moduli. It is shown that the rank of the Yukawa matrix can decrease at specific
loci in complex structure moduli space. In particular, we compute the up Yukawa
coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic
standard model described in arXiv:1404.2767
