The unknown in the diffusion equation is a function u(x, t) of space and time.The physical significance of u depends on what type of process that is described by the diffusion equation. For example, u is the concentration of a substance if the diffusion equation models transport of this substance by diffusion.Diffusion processes are of particular relevance at the microscopic level in biology. The rkc solver is an explicit method with very low memory requirements and a quadratically growing stability region. As such it is able to dynamically select, at each step, the most efficient stable formula. These properties make it ideal for the solution of parabolic partial differential equations using the method of lines. In fact it is.

Partial Differential Equation Toolbox ™ provides functions for solving structural mechanics, heat transfer, and general partial differential equations (PDEs) using finite element analysis.You can perform linear static analysis to compute deformation, stress, and strain. For modeling structural dynamics and vibration, the toolbox provides a direct time integration solver. You can analyze a component’s structural characteristics by performing modal analysis to find natural frequencies and mode shapes. You can model conduction-dominant heat transfer problems to calculate temperature distributions, heat fluxes, and heat flow rates through surfaces. You can also solve standard problems such as diffusion, electrostatics, and magnetostatics, as well as custom PDEs.Partial Differential Equation Toolbox lets you import 2D and 3D geometries from STL or mesh data. You can automatically generate meshes with triangular and tetrahedral elements. You can solve PDEs by using the finite element method, and postprocess results to explore and analyze them.

A bibliography listing all the sources can be found following the last chapter. To simulate the time constraints imposed by the licensing exam, an effective way to use this book is to allow yourself one minute to answer each question in a given chapter. Each answer is accompanied by a specific page reference to a text that provides background to the answer and a short dis cussion of issues raised by the question and answer. After you finish going through the questions in the section, spend as much time as you need verifying your answers and carefully reading the explanations provided.Special attention should be given to the explanations for the questions you answered incorrectly; however, you should read every explanation even if you’ve answered correctly. Immunology pdf book.