Applied Mathematics in Hydrogeology

Preface.- Conservation Equations: Heat Conduction.- Groundwater Flow.- Advective Heat Transfer.- Dispersion Equation.- Boundary and Initial Conditions.- Problems, Keys, and Suggested Readings.- Notations.- Source Functions and Convolution: Heat Sink and Source.- Convolution.- Theis Well Function.- Problems, Keys, and Suggested Readings.- Notations.- Well Functions in Confined Aquifers: Theis Well Function.- Steady-State Solution.- Full-Penetration Pumping Well.- Hantush's Leaky Aquifer.- Leakage at the Boundary.- Slug Test.- Problems, Keys, and Suggested Readings.- Notations.- Well Functions In Unconfined Aquifers: Dupuit-Forchheimer Theory.- Two Dimensional Problems.- Three Dimensional Problems.- Radial Dispersion.- Simulation by Z-Transform.- Problems, Keys, and Suggested Readings.- Notations.- Solving Elementary Matrix Operations: Eigenproblems.- x=A-1b.- Singular Value Decomposition.- Examples.- Problems, Keys, and Suggested Readings.- Bibliography.- Index.

As introduced in Dr. Lee's 10-week class, Applied Mathematics in Hydrogeology is written for professionals and graduate students who have a keen interest in the application of mathematics in hydrogeology.Its first seven chapters cover analytical solutions for problems commonly encountered in the study of quantitative hydrogeology, while the final three chapters focus on solving linear simultaneous equations, finite element analysis, and inversion for parameter determination.Dr. Lee provides various equation-solving methods that are of interest to hydrogeologists, geophysicists, soil scientists, and civil engineers, as well as applied physicists and mathematicians. In the classroom, this same information will help students realize how familiar equations in hydrogeology are derived-an important step toward development of a student's own mathematical models.Unlike other applied mathematics books that are structured according to systematic methodology, Applied Mathematics in Hydrogeology emphasizes equation-solving methods according to topics. Hydrogeological problems and governing differential equations are introduced, including hydraulic responses to pumping in confined and unconfined aquifers, as well as transport of heat and solute in flowing groundwater.

Conservation EquationsSource Functions and ConvolutionLaplace and Hankel TransformsDrawdown in Confined AquifersDrawdown in Unconfined AquifersHeat Transfer and Groundwater FlowSolute TransportSolving Ax=bFinite Element AnalysisInverse ProblemsAppendix: Notes on Equation Solving

Lee, Tien-Chang