- 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
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- About this Textbook
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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.
- About the authors
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Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen
- Reviews
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“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)
- Table of contents (7 chapters)
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Introduction
Pages 1-36
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Systems of Linear Equations
Pages 37-74
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Basic Principles of Thermodynamics
Pages 75-129
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Ordinary Differential Equations
Pages 131-196
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Continuum Mechanics
Pages 197-302
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Table of contents (7 chapters)
- Download Preface 1 PDF (64.5 KB)
- Download Sample pages 1 PDF (338.2 KB)
- Download Table of contents PDF (166.5 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Mathematical Modeling
- Authors
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- Christof Eck
- Harald Garcke
- Peter Knabner
- Series Title
- Springer Undergraduate Mathematics Series
- Copyright
- 2017
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-55161-6
- DOI
- 10.1007/978-3-319-55161-6
- Softcover ISBN
- 978-3-319-55160-9
- Series ISSN
- 1615-2085
- Edition Number
- 1
- Number of Pages
- XV, 509
- Number of Illustrations
- 105 b/w illustrations, 2 illustrations in colour
- Topics
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