Partial Differential Equations in Action

This is the fourth edition of a book whose third edition was reviewed here. Much of the book remains the same, but there has been some re-ordering of topics and a few additions.

 

The treatment of first-order equations has been supplemented by additional discussion of complete, general, and singular solutions. Later on, a treatment of the important topic of reaction-diffusion equations has been added. New exercises in many chapters have also been included.

 

The book remains a very comprehensive treatment of partial differential equations for advanced undergraduates and graduate students. The first five chapters provide a good introduction for undergraduates or students new to the subject. This treats individual classes of equations (first order, diffusion, and Laplace) in some detail. Later chapters expand the treatment and include more advanced material from functional analysis and Sobolev space theory.

 

The authors have aimed this book at students of applied mathematics, physics, and engineering. The book’s title accurately describes the approach that begins in applications and modeling and then carefully fills in the underlying theory.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.