Choice Review

Insofar as solving equations constitutes (some of!) what mathematicians do, the existence of equations that admit no solution at all complicates matters greatly. A time-honored coping strategy consists of enlarging the universe of objects that might provisionally count as solutions. When most equations admit some sort of solution, a cleaner theory results. Within such a theory, one can then factor the solving process into two stages: finding generalized solutions and investigating whether they actually furnish traditional solutions. In ordinary algebra, one expands from real to complex numbers just for finding real roots of real equations. Functions, not numbers, provide potential solutions for differential equations, so distributions (in the sense of this book) provide a class of generalized functions. Distributions usually get an erudite treatment targeted at advanced graduate students or a development-on-the-fly as a tool for solving partial differential equations, for example. Uniquely, this work by Georgiev (Univ. of Sofia, Bulgaria) reads stylistically like a brief, basic, but exotic calculus text, replete with concrete sample calculations. Many researchers found distributions quite alien when they made the scene 65 years ago, but with this book, today's mathematics and physics undergraduate students may well come to regard them as quite routine. Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners. --David V. Feldman, University of New Hampshire