  The future Electron-Ion Collider will utilize high-luminosity high-energy
electron+proton ($e+p$) and electron+nucleus ($e+A$) collisions to solve
several fundamental questions in the high energy nuclear physics field. Heavy
flavor products play an important role in constraining the initial-state
nucleon/nucleus parton distribution functions especially in the high and low
Bjorken-x ($x_{BJ}$) region and exploring the final-state parton propagation
and hadronization processes under different nuclear medium conditions. Latest
simulation studies of heavy flavor hadron and jet measurements with the EIC
project detector conceptual design will be discussed. The projected statistical
accuracy of heavy flavor jet and heavy flavor hadron inside jet measurements in
comparison with latest theoretical calculations will be presented.
