Introduction to the Foundations of Applied Mathematics
Authors: Holmes, Mark H.
 Establishes the mathematical ideas underlying model development independently of a specific application
 Includes a wide spectrum of exercises and detailed illustrations that significantly enrich the material
 Written by a well known author with previous successful books
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 About this Textbook

The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change.
What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book.
The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered.
Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful.
The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition.
Review of first edition:
"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
 About the authors

Mark Holmes is a Professor at Rensselaer Polytechnic Institute, and is currently the Director of the Center for Modeling, Optimization and Computational Analysis. His research interests involve problems integrating modeling and computational analysis. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to the Foundations of Applied Mathematics
 Authors

 Mark H. Holmes
 Series Title
 Texts in Applied Mathematics
 Series Volume
 56
 Copyright
 2019
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030242619
 DOI
 10.1007/9783030242619
 Hardcover ISBN
 9783030242602
 Series ISSN
 09392475
 Edition Number
 2
 Number of Pages
 XVI, 528
 Number of Illustrations
 71 b/w illustrations, 119 illustrations in colour
 Topics