This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more.

Modeled on the popular *Princeton Companion to Mathematics*, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics.

- Features nearly 200 entries organized thematically and written by an international team of distinguished contributors
- Presents the major ideas and branches of applied mathematics in a clear and accessible way
- Explains important mathematical concepts, methods, equations, and applications
- Introduces the language of applied mathematics and the goals of applied mathematical research
- Gives a wide range of examples of mathematical modeling
- Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more
- Explores the connections between applied mathematics and other disciplines
- Includes suggestions for further reading, cross-references, and a comprehensive index

"The treasures [in the *Princeton Companion to Applied Mathematics*] go on and on."**—Lloyd N. Trefethen, ***SIAM Review*

"[An] impressive volume. . . . It has been a major project that eventually resulted in this amazing product."**—Adhemar Bultheel, ***European Mathematical Society*

"Safe to say there is something for everyone in *The Princeton Companion to Applied Mathematics*."**—Alan Stevens, ***Mathematics Today*

"[A] valuable addition to the mathematics library of any university or research institution."**—***Library Journal*

"Higham and his associate editors . . . have produced an admirably readable and informative volume, which anyone interested in applied mathematics would be well advised to consult or—better still—to own!"**—James Case, ***SIAM News*

"A unique work full of beautiful and interesting mathematics. It is surely a valuable resource for exposing young mathematicians to possible areas of applied mathematics for research and further study. Without a doubt *PCAM* is an important contribution to the mathematical literature."**—Jason M. Graham, ***MathSciNet*

"[A]n excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career. . . . As a reader, I find myself flipping through the pages and becoming engaged in new and interesting ideas from the world of applied math."**—Joanna Bieri, ***MAA Reviews*

"A handy one-volume reference for applied mathematics that cuts across several disciplines within an academic framework."**—Lesley S.J. Farmer, ***Reference Reviews*

"Astonishing. . . . As a reference, it is superb. . . . This book took years to produce, and that effort shows in the excellent final product."**—Mark Hunacek, ***Mathematical Gazette*

"This book is an excellent resource for any mathematics departmental library. The articles cover a vast array of different application of mathematics and are . . . well-written with useful reference lists."**—David Graham, ***London Mathematical Society Newsletter*

"Monumental and comprehensive, *The Princeton Companion to Applied Mathematics* does a breathtaking job of conveying the richness, depth, and vitality of today's applied mathematics. Better still, it does so in a remarkably clear and friendly voice. An instant classic."—Steven Strogatz, Cornell University and author of *The Joy of x*

"The perfect companion to the earlier *Companion*. This book will be a landmark for decades ahead."—Nick Trefethen, University of Oxford

"*The Princeton Companion to Applied Mathematics* is a tour de force, an incredible collection that should be on the shelf of every mathematician, of every scientist, and indeed of anyone fascinated with mathematics. It has something for everyone from beginner to advanced researcher, and is written in a style that will encourage reading outside one's area. It is comprehensive, authoritative, and beautifully written and organized, and I know of nothing comparable."—Simon A. Levin, Princeton University and editor of *The Princeton Guide to Ecology*

"This remarkable volume takes on an impossible mission and completes it with style, precision, and scholarship. Collected here are definitive accounts of the major topics in modern applied mathematics by world leaders on the subject. The breadth of topics is enormous. Higham and his collaborators have compiled a special source that will be invaluable to researchers, students, and specialists alike."—J. Tinsley Oden, University of Texas at Austin

"A lot of modern science *is* applied math. Thus, *The Princeton Companion to Applied Mathematics* is a remarkable compendium of insight from across the sciences. Whether you want new insights into your own field or just want to learn something interesting about the world, this book is an ideal place to start."—John H. Miller, Carnegie Mellon University and the Santa Fe Institute

"The editors are distinguished scientists and, perhaps of even more significance for a reference book like this, excellent expositors of mathematics across a range of levels."—Jan Hesthaven, Swiss Federal Institute of Technology in Lausanne

"A welcome contribution to the field."—Andrea L. Bertozzi, University of California, Los Angeles

"There is nothing like *The Princeton Companion to Applied Mathematics*, which will be extremely useful to both researchers and the mathematically inclined public. We have needed a book like this."—Steven Strogatz, author of *The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math*