Find the surface temperature fluctuations of soil as the result of variation of temperature seasonally. when the surface is heated or cooled, the heat will diffuse through the soil. the diffusion can be represented mathematically by the equation: partial differential t(t, z)/partial differential t = k partial differential^2 t(t, z)/partial differential z^2 where t (t, z) is the temperature at the time t and depth z, and k is a constant which measures the diffusivity of the soil (k = 2 times 10^-6 m^2/s). evaluate the t (t, z) for 6 months period by using finite difference approximation using any programming language code that you are familiar with. boundary conditions the top boundary: we specify a temperature that varies seasonally. t(t, 0) = 15 - 10 sin (2 pi t/12) the bottom boundary: we assume that no heat reaches the bottom from the top. partial differential t(t, z)/partial differential z = 0 this specifies that there is 0 heat flow at the bottom. we do not yet know what this bottom temperature will be. the left and right sides of the soil will be regarded as well insulated. plot the heat distribution at depths of 0, 510, 15 and 20 m with time (months). plot the heat distribution for 0-100 m with time