Overview
- Provides a well-structured introduction to the modeling process using mathematical structures as ordering principle
- Contains a wealth of examples from applications in the natural and engineering sciences
- The book starts with simple models based on linear algebra and ends up with complex models involving nonlinear PDEs and free boundaries
- Contains more than 150 exercises with increasing difficulty
- Of use both for undergraduate students as well as experienced researchers which aim to learn about the modeling process
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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About this book
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application.
Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
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Keywords
Table of contents (7 chapters)
Reviews
“Mathematical Modeling is very well written and provides a rigorous introduction to the mathematical modeling of problems from physics and engineering. It is well suited as a text for mathematical modeling courses at the undergraduate and graduate levels that focus on classical deterministic models at continuous scales.” (Laura A. Miller, SIAM Review, Vol. 61 (2), 2019)
“The goal of this book (an English translation of a German text first published about ten years ago) is to teach undergraduate and graduate students the basic examples and techniques of mathematical modeling of real-world phenomena. … for a very well-prepared reader with a willingness to work hard, there is a wealth of interesting material to be found here.” (Mark Hunacek, MAA Reviews, maa.org, July, 2017)
“The goal of this book (an English translation of a German text first published about ten years ago) is to teach undergraduate and graduate students the basic examples and techniques of mathematical modeling of real-world phenomena. … for a very well-prepared reader with a willingness to work hard, there is a wealth of interesting material to be found here.” (Mark Hunacek, MAA Reviews, maa.org, July, 2017)
Authors and Affiliations
About the authors
Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen
Bibliographic Information
Book Title: Mathematical Modeling
Authors: Christof Eck, Harald Garcke, Peter Knabner
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-55161-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-55160-9Published: 21 April 2017
eBook ISBN: 978-3-319-55161-6Published: 11 April 2017
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XV, 509
Number of Illustrations: 105 b/w illustrations, 2 illustrations in colour