Authors:
- 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)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
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.
Reviews
“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
-
Universität Stuttgart, Stuttgart, Germany
Christof Eck
-
Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany
Harald Garcke
-
Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany
Peter Knabner
About the authors
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