Heat Conductionby James M. Hill, Jeff Dewynne
One of the most important partial differential equations in applied mathematics is the heat or diffusion equation. Its importance in the modeling of heat conduction, diffusional processes, and flow through a porous medium is well known. It arises from a probabilistic framework and emerges as the simplest approximation to bulk processes governed at the microscopic level by random spatial variations. Heat Conduction provides a balanced account of solutions and results for the heat equation and serves as a modern undergraduate text that reflects the importance of the heat equation in applied mathematics and mathematical modeling. The first two chapters of the book are introductory and summarize the essential elements of heat flow, diffusion, the mathematical formulation, and simple general results. The next two chapters develop exact analytical solutions, obtained by Laplace transforms and Fourier series, for infinite and finite media problems respectively. Other chapters deal with approximate analytical solutions based on the heat-balance integral method, numerical methods for the heat equation, and simple heat conduction moving boundary problems.
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