Mathematical Modeling [Paperback]

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.-

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)

Prof. Dr. Christof Eck, Prof. Dr. Harald Garcke, Universit?t Regensburg Prof. Dr. Peter Knabner, Universit?t Erlangen

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 lc¶