Mathematical Modeling

Description

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. Front Matter....Pages i-xv Introduction....Pages 1-36 Systems of Linear Equations....Pages 37-74 Basic Principles of Thermodynamics....Pages 75-129 Ordinary Differential Equations....Pages 131-196 Continuum Mechanics....Pages 197-302 Partial Differential Equations....Pages 303-426 Free Boundary Problems....Pages 427-487 Back Matter....Pages 489-509