Read more
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.
List of contents
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.-
About the author
Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen
Summary
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.
Additional text
“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)
Report
"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)
