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© 2016

Mathematical Modelling

  • Seppo Pohjolainen
Textbook

Table of contents

  1. Front Matter
    Pages i-xi
    PDF
  2. Introduction
    Seppo Pohjolainen, Matti Heiliö
    Pages 1-5
  3. Models and Applications
    Matti Heiliö
    Pages 7-23
  4. Viewpoints on Systems and Models
    Erkki Laitinen
    Pages 25-34
  5. Integer Models
    Risto Silvennoinen, Jorma Merikoski
    Pages 35-54
  6. Data Based Models
    Jorma Merikoski
    Pages 55-78
  7. Soft Computing Methods
    Esko Turunen, Kimmo Raivio, Timo Mantere
    Pages 79-112
  8. Dimensional Analysis
    Timo Tiihonen
    Pages 113-121
  9. Modelling with Differential Equations
    Jukka Tuomela
    Pages 123-148
  10. Continuum Models
    Timo Tiihonen
    Pages 149-170
  11. Simplification of Models
    Timo Tiihonen
    Pages 171-183
  12. Acoustic Modelling
    Seppo Pohjolainen, Antti Suutala
    Pages 185-205
  13. Inverse Problems
    Marko Vauhkonen, Tanja Tarvainen, Timo Lähivaara
    Pages 207-227
  14. Project Titles
    Matti Heiliö
    Pages 229-237
  15. Back Matter
    Pages 239-242
    PDF

About this book

Introduction

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. 

The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.  

Keywords

acoustical modeling data based models differential equations dimensional analysis dontinuum models fuzzy logic genetic algorithms integer models inverse problems mathematical modelling network models neural computation perturbation methods soft computing teaching of modelling

Authors and affiliations

  1. 1.School on Engineering ScienceLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Department of Applied PhysicsUniversity of Eastern FinlandKuopioFinland
  3. 3.Department of Mathematical SciencesUniversity of OuluOuluFinland
  4. 4.Department of Computer ScienceUniversity of VaasaVaasaFinland
  5. 5.School of Information SciencesUniversity of TampereTampereFinland
  6. 6.Department of MathematicsTampere University of TechnologyTampereFinland
  7. 7.Huawei TechnologiesHelsinkiFinland
  8. 8.Department of MathematicsTampere University of TechnologyTampereFinland
  9. 9.Department of MathematicsTampere University of TechnologyTampereFinland
  10. 10.Department of Applied PhysicsUniversity of Eastern FinlandKuopioFinland
  11. 11.Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland
  12. 12.Department of Physics and MathematicsUniversity of Eastern FinlandJoensuuFinland
  13. 13.Department of MathematicsTampere University of TechnologyTampereFinland
  14. 14.Department of Applied PhysicsUniversity of Eastern FinlandKuopioFinland

Editors and affiliations

  • Seppo Pohjolainen
    • 1
  1. 1.Tampere University of Technology Department of MathematicsTampereFinland

About the editors

Seppo Pohjolainen received his PhD degree in applied mathematics in 1980 from Tampere University of Technology (TUT). In 1998 he was appointed as a professor in mathematics at TUT.   

His research interests include mathematical control theory, distributed parameter systems, mathematical modelling and simulation, development and use of information technology to support learning. Currently he is leading a nationwide network in Finland on teaching mathematical modelling on the Internet. He has led several national and international research projects and written a number of journal articles and conference papers on all these fields. 

 


                          

Bibliographic information

Reviews

“Mathematical modelling is a product of several different contributors, all from Finnish universities. The result is a text used by over 2,000 students. … This is an excellent book, written with a myriad of interesting and very practical problems and applications. The contributors to the text are obviously scientific scholars who are elegantly educated.” (James Van Speybroeck, Computing Reviews, March, 2017)