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
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
Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen
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.
1Introduction.-
2 Systems of Linear Equations.-
3 Basic Principles of Thermodynamics.-
4 Ordinary Differential Equations.-
5 Continuum Mechanics.-
6 Partial Differential Equations.-
7 Free Boundary Problems.-
"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)
"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)
Über den Autor
Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen
Inhaltsverzeichnis
1Introduction.-
2 Systems of Linear Equations.-
3 Basic Principles of Thermodynamics.-
4 Ordinary Differential Equations.-
5 Continuum Mechanics.-
6 Partial Differential Equations.-
7 Free Boundary Problems.-
Klappentext
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.n nMethods 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.
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
