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Modelling with the Master Equation

Solution Methods and Applications in Social and Natural Sciences


  • Offers self-contained introduction to the mathematical and statistical fundamentals of the Master equation and a toolbox for further applications

  • Explains the modelling potential of the Master equation in detail by means of many examples from different disciplines

  • Documents and discusses all relevant mathematical steps, helping the reader to apply the method quickly


Table of contents

  1. Front Matter
    Pages i-xxv
  2. Günter Haag
    Pages 1-11
  3. Statistical Toolbox

    1. Front Matter
      Pages 13-13
    2. Günter Haag
      Pages 15-37
    3. Günter Haag
      Pages 63-91
  4. Applications Natural Sciences

    1. Front Matter
      Pages 93-93
    2. Günter Haag
      Pages 95-139
  5. Applications Social Sciences

    1. Front Matter
      Pages 141-141
    2. Günter Haag
      Pages 181-232
    3. Günter Haag
      Pages 233-303

About this book


This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples.

Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences.

The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach.  

Drawing upon the author’s extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.


Master Equation Modelling Social Sciences Model Building Fokker-Planck Equation Population Dynamics Dynamic Decision Theory Econophysics-Migration-Urban Dynamics Transport

Authors and affiliations

  1. 1.Institute of Theoretical Physics IIUniversity of StuttgartGermany

About the authors

Guenter Haag studied engineering and physics at the University of Stuttgart and earned his Ph. D in Physics in 1978. He was visiting professor at the Case Western Reserve University, Cleveland in 1982 and the Institute for Advanced Studies (IHS), Vienna in 1990. At that time he was also member of the working groups Long waves in economy and Metropolitan studies at the International Institute for Applied Systems Analysis (IIASA), Laxenburg. The appointment to a university lectureship came in 1985 and in 1995 he was appointed APL professor for Theoretical Physics at the University of Stuttgart. In 1993 he became in addition managing director of the Institute for Applied Economic Research, Tuebingen. Two years later he founded the Steinbeis Transfer Center Applied Systems Analysis in Stuttgart, and in 2003 the STASA GmbH. He is member of different international working groups and member in the editorial board of international journals. He has initiated and led several national and international projects in the field of system analysis, statistics, urban and regional development and transport theory. Robert-Mayer-Award, do-it Software-Award 2004,  Löhn-Award 2011. 

Bibliographic information

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