Mathematics Applied to Deterministic Problems in the Natural Sciences

by C.C. Lin, L.A. Segel

Addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences. The authors' case studies approach leads to excitement in teaching realistic problems. The exercises reinforce, test and extend the reader's understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.

Genres: Mathematics

630 pages, Paperback

First published December 1, 1988

About the author

C. C. Lin was Institute Professor Emeritus in Applied Mathematics at MIT and Distinguished Professor at Tsinghua University in China.

Reviews

[Conrad · Rating 5 out of 5]

"'Applied Mathematics' is an insult, directed by those who consider themselves 'pure' mathematicians, at those whom they take for impure. Mathematics is, always has been, and always will be pure mathematics. The adjective 'pure' is redundant. The very essence of mathematics is abstraction, created by fancy and tempered by rigor, but 'pure mathematics' as a parricide tantrum denying growth from human sensation, as a shibboleth to cast out the impure, is a disease invented in the last century" C. Truesdell, "The Modern Spirit in Applied Mathematics," ICSU Rev. World Sci. 6, 195-205 (1964)

More than any other words I have read these words have lodged in my mind. In one go Truesdell simultaneously laid bare the sociological condition of mathematics in the twentieth century, and did so with language that is uncommonly artful. In the first chapter of Mathematics Applied to Deterministic Problems in the Natural Sciences, Lin and Segel ask "What is applied mathematics?" They present us with Truesdell's quote as one possible view of applied mathematics. It seems to me that Lin and Segel's own outlook is similar to Truesdell's, and considering that this is not the first time I have run across this quote, it seems that this is the way many applied mathematicians think of their own discipline.

Unlike those mass marketed textbooks, stamped with the title Applied Mathematics, and pushed onto unfortunate students by textbook publishers, this one is not a collection of canned techniques. Although the authors limited their scope to the analysis, and interpretation of deterministic models in the natural sciences, this choice was necessary to constrain the size of their book. But the particular techniques presented are not as important as their approach. Lin and Segel have a clear message about how we should think about applied mathematics.

They want us to experience applied mathematics as a unified whole where problems posed by the sciences are stripped to some conceptual core, and at this core we can see those abstract qualities which link problems in widely disparate fields. For instance, to have us see this process they start with the examples of the clustering of stars in the formation of galaxies and of aggregates of slime mold, and they invite us to examine the abstract commonalities between these two processes. Throughout we repeatedly see the same problem from the physical or biological sciences viewed from different angles, and we see a mathematical technique applied to several scientific problems. As a former student I found this teaching philosophy much more inviting, and ultimately more enlightening than a list of canned techniques. It really is an unfortunate consequence of how textbooks are currently being created and marketed, that books that allow the student to see the bigger picture of their subject are so rare.