  The density dependence of nuclear symmetry energy is determined from a
systematic study of the isospin dependent bulk properties of asymmetric nuclear
matter using the isoscalar and the isovector components of density dependent
M3Y interaction. The incompressibility $K_\infty$ for the symmetric nuclear
matter, the isospin dependent part $K_{asy}$ of the isobaric incompressibility
and the slope $L$ are all in excellent agreement with the constraints recently
extracted from measured isotopic dependence of the giant monopole resonances in
even-A Sn isotopes, from the neutron skin thickness of nuclei and from analyses
of experimental data on isospin diffusion and isotopic scaling in intermediate
energy heavy-ion collisions. This work provides a fundamental basis for the
understanding of nuclear matter under extreme conditions, and validates the
important empirical constraints obtained from recent experimental data.
