1 The Diffusion Equation.- 2 Reaction—Advection—Dispersion Equation.- 3 Traveling Wave Solutions.- 4 Filtration Models.- 5 Subsurface Flow Dynamics.- 6 Transport and Reactions in Rocks.- A The Finite-Difference Method.- B The Method of Lines.- C Numerical Inversion of Transforms.- D Notation and Symbols.- References.
The subject of this monograph lies in the joint areas of applied mathematics and hydrogeology. The goals are to introduce various mathematical techniques and ideas to applied scientists while at the same time to reveal to applied math ematicians an exciting catalog of interesting equations and examples, some of which have not undergone the rigors of mathematical analysis. Of course, there is a danger in a dual endeavor-the applied scientist may feel the mathematical models lack physical depth and the mathematician may think the mathematics is trivial. However, mathematical modeling has established itself firmly as a tool that can not only lead to greater understanding of the science, but can also be a catalyst for the advancement of science. I hope the presentation, written in the spirit of mathematical modeling, has a balance that bridges these two areas and spawns some cross-fertilization. Notwithstanding, the reader should fully understand the idea of a mathe matical model. In the world of reality we are often faced with describing and predicting the results of experiments. A mathematical model is a set of equa tions that encapsulates reality; it is a caricature of the real physical system that aids in our understanding of real phenomena. A good model extracts the essen tial features of the problem and lays out, in a simple manner, those processes and interactions that are important. By design, mathematical models should have predictive capability.
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