Introduction to the Foundations of Applied Mathematics
Authors: Holmes, Mark Hayden
Free Preview- 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
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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
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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.
- Table of contents (9 chapters)
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Dimensional Analysis
Pages 1-47
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Perturbation Methods
Pages 49-101
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Kinetics
Pages 103-164
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Diffusion
Pages 165-232
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Traffic Flow
Pages 233-294
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Introduction to the Foundations of Applied Mathematics
- Authors
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- Mark Hayden Holmes
- Series Title
- Texts in Applied Mathematics
- Series Volume
- 56
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-24261-9
- DOI
- 10.1007/978-3-030-24261-9
- Hardcover ISBN
- 978-3-030-24260-2
- Softcover ISBN
- 978-3-030-24263-3
- Series ISSN
- 0939-2475
- Edition Number
- 2
- Number of Pages
- XVI, 528
- Number of Illustrations
- 70 b/w illustrations, 120 illustrations in colour
- Topics
