Introduction to the Foundations of Applied Mathematics

1. Front Matter

   Pages i-xiv

   PDF

2. Dimensional Analysis

   • Mark H. Holmes

   Pages 1-42

3. Perturbation Methods

   • Mark H. Holmes

   Pages 43-85

4. Kinetics

   • Mark H. Holmes

   Pages 87-140

5. Diffusion

   • Mark H. Holmes

   Pages 141-203

6. Traffic Flow

   • Mark H. Holmes

   Pages 205-264

7. Continuum Mechanics: One Spatial Dimension

   • Mark H. Holmes

   Pages 265-310

8. Elastic and Viscoelastic Materials

   • Mark H. Holmes

   Pages 311-349

9. Continuum Mechanics: Three Spatial Dimensions

   • Mark H. Holmes

   Pages 351-401

10. Fluids

    • Mark H. Holmes

    Pages 403-440

11. Back Matter

    Pages 441-468

    PDF

FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.

• Applied Mathematics
• Foundations
• Identity
• Introduction
• calculus
• equation
• linear optimization
• mathematics
• theorem

From the reviews:

“This work by Holmes (RPI) is a thorough overview of classical analysis/differential equations-based applied mathematics (not statistics or discrete mathematics). … This is a wonderful, well-written book that should be in every academic library. Includes many examples, 126 references, and 221 exercises. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, researchers, and faculty.” (J. D. Fehribach, Choice, Vol. 47 (8), April, 2010)

“The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. … Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. … One of the best features of the book is the abundant number of exercises found at the end of each chapter. … I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers.” (Joe Latulippe, The Mathematical Association of America, December, 2009)

“One of the primary objectives of the book is to use mathematics to derive a fundamental understanding of the derivation, analysis and interpretation of mathematical models. … The book contains a wide spectrum of exercises and detailed illustrations. It addresses students and researchers interested in mathematical modeling in physics, engineering and applied sciences. It can also be recommended as a textbook at the graduate student level.”­­­ (Iuliana Oprea, Mathematical Reviews, Issue 2011 c)

“Holmes’s text … should be accessible to both mathematicians and science and engineering audiences at the senior or beginning graduate level. … it establishes the tools of applied mathematics and the underlying concepts of model development independent of a specific application. … I strongly recommend this book for an introductory senior or graduate level course in applied mathematics.” (J.David Logan, SIAM Review, Vol. 52 (1), 2010)

• Academic Science of the Material, Science and Engineering, Rensselaer Polytechnic Institute, Troy, U.S.A.

  Mark H. Holmes

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