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.

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

Autorentext

Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universität Regensburg Prof. Dr. Peter Knabner, Universität Erlangen

Inhalt
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.-