Includes bibliographical references (pages 526-538) and index.

1. Mass balance, mixing, and fractionation. Concentrations as mixing variables. Reactional assemblage. Working with ratios. Normalized variables. Incremental processes (distillation) -- 2. Linear algebra. A matrix refresher. Square matrices. Eigencomponents. Quadratic forms and associated quadrics. Systems of linear differential equations. Linear function spaces -- 3. Useful numerical analysis. Functions of a single variable. Functions of several variables. Partial differential equations: the finite differences method -- 4. Probability and statistics. A single random variable. Several random variables. Error propagation and error calculation. Principal component analysis -- 5. Inverse methods. Linear estimates. Non-linear least-squares. Constrained least-squares. Handling errors in least-square problems. Gradient projection and the total inverse. The continuous inverse model -- 6. Modeling chemical equilibrium. The Newton-Raphson method applied to solutions. Gibbs energy minimization -- 7. Dynamic systems. Single-variable residence time analysis. One element in several interacting reservoirs. Several elements in several interacting reservoirs -- 8. Transport, advection, and diffusion. Fluxes. The divergence theorem and the conservation equations. Advection and percolation. Diffusion basics. Solutions of the diffusion equation: parallel flux. Radial flux and spherical coordinates. The diffusion coefficient varies with time. Two useful steady-state solutions. Simultaneous precipitation and diffusion -- Appendix 8A: The error function -- Appendix 8B: The theta functions -- Appendix 8C: Duhamel's principle -- 9. Trace elements in magmatic processes. Batch-melting and crystallization. Incremental processes. Open magmatic systems. Which element, which process? Disequilibrium fractionation during crystal growth.