Show all reasoning and intermediate results leading to your answer, or credit will be lost. One book of mathematical tables, such as Schaum's Mathematical Handbook, may be used, as well as a calculator and one handwritten letter-size single formula sheet.
Draw the characteristics very neatly. Using your picture, explain where in the -plane the derived solution can reasonably be assumed to apply, and where it is indeterminate or likely not to be correct.
convection-diffusion problemin a semi-infinite pipe, in which the flow velocity at one end of the pipe is given:
Use only the attached Laplace transform tables unless stated otherwise. List the items in the tables used. No convolution unless it is unavoidable.
At the end, write out the fully worked out solution completely, with all parameters in it clearly identified. List all eigenfunctions and eigenvalues and Fourier coefficients completely.